Learning with Leanne
Learning with Leanne
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Change of Basis (using coordinate isomorphism)
Linear Algebra Pt.22
0:00 Matrix of Transformation with Standard Basis of R2
0:44 Matrix of Transformation with Standard Basis of P2
0:56 Intro to Coordinate Isomorphism
2:07 Matrix of Transformation with Standard Basis of P2 Continued...
3:07 Ex - Find coordinates of matrix in terms of basis B
4:29 Commutative Diagram
6:22 Ex - Find the Transformation (given matrix of T in terms of non-standard bases)
8:59 Ex - The Plan: Find the matrix of T in terms of B and D (non-standard bases)
9:32 Ex - Method #1: Find the matrix of T in terms of B and D (non-standard bases)
11:05 Ex - Method #2: Find the matrix of T in terms of B and D (non-standard bases)
Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html
1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html
2. Is it a Vector Space? (featuring crazy addition and multiplication rule) ua-cam.com/video/RcjBbuRikMY/v-deo.html
3. Extra Vector Space Properties & Proofs ua-cam.com/video/Qigr7sF9X7Y/v-deo.html
4. Subspace Test Shortcut (and examples) ua-cam.com/video/b50ys-uu33E/v-deo.html
5. Span! Why is it the smallest subspace? When are 2 spans equal? ua-cam.com/video/TjhLGIuXiac/v-deo.html
6. Linearly Independent or Dependent? ua-cam.com/video/pfrBHwGHUy0/v-deo.html
7. Basis, Standard Basis, Dimension? (& finding multiple bases) ua-cam.com/video/jQK_hE7nKQU/v-deo.html
8. Carving & Enlarging Set to find a Basis (with the independent + dependent lemma) ua-cam.com/video/W8axZxJSwFU/v-deo.html
9. Row vs Column space of a matrix ua-cam.com/video/9-besQN5tAg/v-deo.html
10. What’s a LINEAR Transformation? Linear Operator? Matrix of a Transformation? ua-cam.com/video/svAhfMxYSfs/v-deo.html
11. Kernel, Image & Dimension of Transformations Explained! ua-cam.com/video/mEsy0t5NbrM/v-deo.html
12. Injectivity, Surjectivity & Bijectivity made easy ua-cam.com/video/GELXmNO3ghg/v-deo.html
13. Isomorphisms? Coordinate Isomorphisms? Proving linearity & bijection! ua-cam.com/video/GELXmNO3ghg/v-deo.html
14. Composition of linear transformations, Finding T INVERSE ua-cam.com/video/L7g04DbI0V0/v-deo.html
15.Orthogonality? Normalization? Expansion Theorem! ua-cam.com/video/mmQyOD13zxs/v-deo.html
16. Converting to an Orthogonal Basis! How “nice” ua-cam.com/video/BoskFp4MitY/v-deo.html
17. Orthogonal Projections (featuring U + U perp) ua-cam.com/video/ZLDiXB255h4/v-deo.html
18. Similar Matrices, Properties & Proofs ua-cam.com/video/_nh7NBvLaD4/v-deo.html
19. Diagonalization (And what actually are Eigenvalues, Eigenvectors and Eigenspaces?) ua-cam.com/video/HGco-NMYozk/v-deo.html
20. Showing Similarity when A~D and B~D ua-cam.com/video/ziLfoAX1h1Y/v-deo.html
21. Orthogonal Diagonalization ua-cam.com/video/w_kJv1Kbp9A/v-deo.html
22. Change of Basis (using coordinate isomorphism) ua-cam.com/video/WurXWKBOB9c/v-deo.html
Переглядів: 410

Відео

Orthogonal Diagonalization
Переглядів 2 тис.Рік тому
Linear Algebra Pt.21 0:00 When is a matrix Orthogonal? 1:29 When is a matrix Orthogonally Diagonalizable? 2:27 Steps to find P (Orthogonal Diagonalizing Matrix) 3:03 Ex - Step 1: Find Eigenvalues 4:07 Ex - Step 2: Find Eigenvectors & Eigenspaces 6:12 Ex - Step 3: Orthonormalize the Eigenvectors (Gram-Schmidt Algorithm) 7:36 Ex - Step 4: Build P and D! Linear Algebra Playlist: ua-cam.com/play/PL...
Showing Similarity when A~D and B~D
Переглядів 99Рік тому
Linear Algebra Pt.20 0:00 The Plan 0:52 Finding Eigenvalues 1:36 Finding Eigenvectors & Basis of Eigenspaces 3:44 Form D and Diagonalizing matrices 4:57 How to check your work? 5:37 Ex - Find P and P-1 that conjugate matrix A Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html 2. Is it a ...
Diagonalization (And what actually are Eigenvalues, Eigenvectors and Eigenspaces?)
Переглядів 196Рік тому
Linear Algebra Pt.19 0:00 When is a Matrix Diagonalizable? 0:30 What are Eigenvalues & Eigenvectors? 2:38 How to find Eigenvalues & Eigenvectors? 3:47 Eigenspace! And how to find a basis? 5:10 Properties of Diagonalizable Matrices 5:56 Ex - Is A Diagonalizable? Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/vide...
Similar Matrices, Properties & Proofs
Переглядів 310Рік тому
Linear Algebra Pt.18 0:00 What to Similar Matrices have in Common? 0:57 Equivalence Relation (and Proofs) 2:57 Additional Properties (and Proofs) 4:37 Ex - Show 2 matrices are NOT similar Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html 2. Is it a Vector Space? (featuring crazy additio...
Orthogonal Projections (featuring U + U perp)
Переглядів 232Рік тому
Linear Algebra Pt.17 0:00 Orthogonal Complement (Perpendicular Subspace) 1:15 Projection onto a Subspace (decomposition into vector in U vector in U perp) 2:41 Ex - Find orthogonal basis of U and vector in U closest to x 4:40 Ex - Write x as a sum of a vector in U and U perp Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples u...
Converting to an Orthogonal Basis! How "nice"
Переглядів 299Рік тому
Linear Algebra Pt.16 0:00 Why can we convert any Basis to an Orthogonal Basis? 0:56 Gram-Schmidt Algorithm (Steps Explained) 1:43 Ex - Find Orthogonal Basis of Subspace (Step 1: Carve out a basis) 3:17 Ex - Find Orthogonal Basis of Subspace (Step 2: Orthogonalize basis) Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam...
Orthogonality? Normalization? Expansion Theorem!
Переглядів 213Рік тому
Linear Algebra Pt.15 0:00 Orthogonal Vectors? 0:41 Orthogonal vs Independent Non-Orthogonal Set 0:59 Dot Product Properties 1:45 Orthonormal Vectors? 2:03 How to Normalize a Vector 2:31 Expanding Vector in terms of Orthonormal Basis Vectors 3:21 Visual Understanding (Dot products Projections) 4:17 Ex - Prove a Set is a Basis using Orthogonality Dimension 5:01 Ex - Express Vector as linear combo...
Composition of linear transformations, Finding T INVERSE
Переглядів 192Рік тому
Linear Algebra Pt.14 0:00 Composition of Linear Transformations 1:19 Inverse Transformations 2:51 Ex - Find T inverse using a matrix (Method #1) 4:52 Ex - Find T inverse directly (Method #2) Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html 2. Is it a Vector Space? (featuring crazy addi...
Isomorphisms? Coordinate Isomorphisms? Proving linearity & bijection!
Переглядів 249Рік тому
Linear Algebra Pt.13 0:00 What is an Isomorphism? 1:08 Properties 2:53 Equivalence Relation 3:19 How to show a Transformation is Isomorphic? 4:40 Ex - Is T Isomorphic? 6:52 Ex- Find an Isomorphism Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html 2. Is it a Vector Space? (featuring craz...
Injectivity, Surjectivity & Bijectivity made easy
Переглядів 257Рік тому
Linear Algebra Pt.12 0:00 Injectivity Explained (a.k.a. one-to-one) 2:06 Surjectivity Explained (a.k.a. onto) 3:44 Bijectivity Explained 4:48 Ex - Show T is linear and surjective, dim of Ker T? Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html 2. Is it a Vector Space? (featuring crazy a...
Kernel, Image & Dimension of Transformations Explained!
Переглядів 1 тис.Рік тому
Linear Algebra Pt.11 0:00 What are the Kernel & Image Visually? 0:52 Walkthrough - Finding Basis of Im T and Ker T 3:51 Rank Nullity = Dim (V) 4:35 Basis of Im T (special case shortcut) 5:10 Ex - Find Basis of M22 including Ker T 8:00 Ex - Finding Basis of Im T (Method #1) 8:51 Ex - Finding Basis of Im T (Method #2) Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.htm...
What's a LINEAR transformation? Linear operator? Matrix of a transformation?
Переглядів 427Рік тому
Linear Algebra Pt.10 0:00 What are Linear Transformations? 1:14 Properties 1:55 Ex - Is Transposition Linear? 4:01 Ex - Define the Transformation 6:19 Matrix of a Transformation Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html 2. Is it a Vector Space? (featuring crazy addition and mult...
Row vs Column space of a matrix
Переглядів 643Рік тому
Linear Algebra Pt.9 0:00 What's the Row Space? 0:29 What'e the Column Space? 0:44 Basis of Row A and Col A? 2:00 Rank Theorem 2:54 Ex - Find Rank, Basis of Row & Column Space Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html 2. Is it a Vector Space? (featuring crazy addition and multipl...
Carving & Enlarging Set to find a Basis (with the independent + dependent lemma)
Переглядів 158Рік тому
Linear Algebra Pt.8 0:00 When to Reduce a set to form a basis 0:36 When to Enlarge a set to form a basis 0:55 Independent Lemma 1:38 Dependent Lemma 2:29 Ex - Carve a Basis from a Spanning Set 5:37 Ex - Expand a Set to form a Basis Linear Algebra Playlist: ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html 1. Vector Space Walkthrough & examples ua-cam.com/video/XJ0h6bh_5Pw/v-deo.html 2. Is...
Basis, Standard bases, Dimension? (& finding multiple bases)
Переглядів 148Рік тому
Basis, Standard bases, Dimension? (& finding multiple bases)
Linearly Independent or Dependent?
Переглядів 88Рік тому
Linearly Independent or Dependent?
Span! Why is it the smallest subspace? When are 2 spans equal?
Переглядів 619Рік тому
Span! Why is it the smallest subspace? When are 2 spans equal?
Subspace Test Shortcut (and examples)
Переглядів 204Рік тому
Subspace Test Shortcut (and examples)
Extra Vector Space Properties & Proofs
Переглядів 249Рік тому
Extra Vector Space Properties & Proofs
Is it a Vector Space? (featuring crazy addition and multiplication rule)
Переглядів 830Рік тому
Is it a Vector Space? (featuring crazy addition and multiplication rule)
Vector Space Axioms Walkthrough & examples
Переглядів 1,9 тис.Рік тому
Vector Space Axioms Walkthrough & examples
Crochet LETTERS (Pt.1 A-G)
Переглядів 209Рік тому
Crochet LETTERS (Pt.1 A-G)
Working with NEGATIVES (most common problem for math students)
Переглядів 1042 роки тому
Working with NEGATIVES (most common problem for math students)
Amigurumi Graduation Hat!!!
Переглядів 13 тис.2 роки тому
Amigurumi Graduation Hat!!!
Amigurumi Hamburger (Customizable & Realistic)
Переглядів 1,8 тис.2 роки тому
Amigurumi Hamburger (Customizable & Realistic)
Adding, Multiplying & Rationalizing Radicals
Переглядів 992 роки тому
Adding, Multiplying & Rationalizing Radicals
House Hunters Parody (Seller's Market in Canada)
Переглядів 3762 роки тому
House Hunters Parody (Seller's Market in Canada)
Amigurumi 101 for Beginners (learn the simple stitches while making a gumball)
Переглядів 2472 роки тому
Amigurumi 101 for Beginners (learn the simple stitches while making a gumball)
Amigurumi Cupcake (cute & easy)
Переглядів 3,8 тис.2 роки тому
Amigurumi Cupcake (cute & easy)

КОМЕНТАРІ

  • @cageyg5642
    @cageyg5642 23 дні тому

    Note to self--- finished first row of d. green 9:07 using 3.75 mm hook

  • @luisdiscua3296
    @luisdiscua3296 Місяць тому

    Holy moly, your explication helps so much. I’ve read my notes and the book and it’s just paragraphs without any real explanation. You’re the best!

  • @angiecampbell1554
    @angiecampbell1554 4 місяці тому

    Hi Leanne, my daughter is struggling with Maths and will be sitting her Nat5 (Scotland) next May 25. I wondered if you are still tutoring and what your cost are? Many thanks.

  • @johantchassem1553
    @johantchassem1553 4 місяці тому

    Thanks very clear explanation

  • @wendyelter600
    @wendyelter600 5 місяців тому

    Thanks that is a great tutorial 😊

  • @melontusk7358
    @melontusk7358 5 місяців тому

    This helps a lot. Thanks so much.

  • @emilygaughan
    @emilygaughan 5 місяців тому

    Love this pattern! Thank you, it's adorable :D

  • @Karen822
    @Karen822 6 місяців тому

    So cute!!❤🎓

  • @jayamazumdar3129
    @jayamazumdar3129 6 місяців тому

    Very nice.👌

  • @pianoguy8927
    @pianoguy8927 6 місяців тому

    Is this beginner friendly?

  • @lina.and.a
    @lina.and.a 6 місяців тому

    Thank you for explanation! You save my exam. Litterally, what we should call girl math <3

  • @rgiorda78
    @rgiorda78 6 місяців тому

    Thanks for sharing this fun tutorial. My banana turned out great!

  • @alexacruz5239
    @alexacruz5239 7 місяців тому

    Help my stitches aren’t as straight as yours lol

  • @Babakiprincess-dq12
    @Babakiprincess-dq12 7 місяців тому

    ❤❤

  • @dyanelopez8221
    @dyanelopez8221 7 місяців тому

    You are great teacher wow, I got it through first time, very easy to understand, an accurate number of Stitches, no music👏👏 Hank you. Very pretty final project. Thank you

  • @faebrowne2537
    @faebrowne2537 7 місяців тому

    I had to watch this with the volume off because the music is horrendous BUT Great pattern and your work is very neat.❤

  • @evanaschaub5054
    @evanaschaub5054 8 місяців тому

    Great video thank you!❤

  • @rosanneholt6377
    @rosanneholt6377 8 місяців тому

    Easy to follow directions. My cupcake looks great. Thank you

  • @nahidasultana6842
    @nahidasultana6842 8 місяців тому

    Hi! I need a math teacher for my daughter. 9th grade (Geometry). Do you teach 101? How much do you charge for hr?

    • @LearningwithLeanne
      @LearningwithLeanne 8 місяців тому

      Hi, I do tutor grade 9 math, however at the moment I am fully booked. Sorry for any inconvenience.

  • @Rostignac
    @Rostignac 9 місяців тому

    Thanks you’re better than my teacher!!!

  • @Cheese4598
    @Cheese4598 9 місяців тому

    Thank you so much for this video, I just wanted you to know that you are extremely underrated, and breathtaking pretty. I have been searching for a good lemon pattern for a while, but this is definitely my favorite. Thank you so much for making this video 🥰

  • @arturobalcazar8567
    @arturobalcazar8567 9 місяців тому

    Hello. My daughter is struggling with trigonometry and asked if she could get a tutor. Are you stiil providing tutoring sessions via zoom?

    • @LearningwithLeanne
      @LearningwithLeanne 9 місяців тому

      Hi, feel free to fill out this form if you are still looking for a tutor forms.gle/W7UKbznsvGohu7Dt7

  • @tamiadeniji
    @tamiadeniji 9 місяців тому

    This is the first time i actually understood vector space, the explanation was very detailed and easy to comprehend. Thank you so much.

  • @anya9423
    @anya9423 10 місяців тому

    Very clear instructions, thank you so much! I have a cute tiny doughnut now!!!

  • @dianaashcraft3364
    @dianaashcraft3364 10 місяців тому

    May I make a comment- move your camera do it records your hand just like your eyes are looking at your hands. Watching you crochet upside down is impossible to follow.

  • @Nils-d-Const
    @Nils-d-Const 11 місяців тому

    the pre-stage of any "crazy" vector space over a field is the hidden affine (translation and/or scalation) transformation map

  • @donnas2375
    @donnas2375 Рік тому

    Thank you, so cute!

  • @CharlesbenoitUsabimana
    @CharlesbenoitUsabimana Рік тому

    Orthogonally diagonalize the matrix 𝐴 = ( 2 2 1 2 5 2 1 2 2 ). Find a way of triangularizing it how can do this

  • @cherrichai
    @cherrichai Рік тому

    love it, tutorial is nice and fast!

  • @xbz24
    @xbz24 Рік тому

    thank you goddess, you saved my life

  • @shannonsprinkle3029
    @shannonsprinkle3029 Рік тому

    I absolutely loved making this banana! Here’s the written pattern for the body of it in case anyone wants it 1: MR 4 sc 2: 4 sc 3: in (8) 4: [in sc] (12) 5: [in 2sc] (16) 6: sc (16) 7: [in 3sc] (20) 8-9: sc (20) x2 10: [dec, 8sc, in, 9sc] (20) 11: sc (20) 12-15: repeat rows 10 and 11 x2 16-18: sc (20) x3

  • @sierra14hope
    @sierra14hope Рік тому

    It's so confusing at 4:25 I can't figure out how many there should be. 10? 6? 12? We go from 12 sc to skipping 4 and ch 6 but then I'd have 14 not 10 🤯

  • @christineneedham2187
    @christineneedham2187 Рік тому

    I love this pattern

  • @christineneedham2187
    @christineneedham2187 Рік тому

    On icing where u slip stitch then say in the 2nd stitch do a sc and a half dbl. Do u skip a stitch after u slip stitch or is the slip stitch the 1st stitch then the 2nd stitch u do a single cro and a half double.

  • @terrieridgley7557
    @terrieridgley7557 Рік тому

    Thank you so much for this tutorial! You were very specific, patient, and made it so much less frustrating! Best one I've found. 💚 exactly what I was looking for. I'm making it for one of my grandson's for his 1st birthday, among other items😊 so happy.

  • @natureislifesounds5518
    @natureislifesounds5518 Рік тому

    That's so cute!! ❤

  • @luciennehofstetter8680
    @luciennehofstetter8680 Рік тому

    Thank you so much for this Video …so cool 🥰

  • @sophievilleneuve4507
    @sophievilleneuve4507 Рік тому

    I cant comment on the donut video but i made a giant donut with chenille yarn using your tutorial and its just AWESOME! You explained really well thank you so much!

  • @umarednan273
    @umarednan273 Рік тому

    I tried this pattern. And it turned out really good. Especially i like your way of showing each and every step so clear that there was no confusion. Thanku

  • @whatsoever4290
    @whatsoever4290 Рік тому

    why can't I get this done? 😢

  • @sabrinabundy8669
    @sabrinabundy8669 Рік тому

    Can I start with red yarn and add black button for center of poppy ?

  • @a.z.6276
    @a.z.6276 Рік тому

    You are very good at explaining things in a short amount of time! Thanks for the video

    • @LearningwithLeanne
      @LearningwithLeanne Рік тому

      Thank you so much! I am very excited to share that I just posted a full linear algebra series if you are interested. The video quality is much better now 😂! ua-cam.com/play/PLP_iTciEpA826mGQ8PotCPNkVEfY1KQGL.html

    • @a.z.6276
      @a.z.6276 Рік тому

      @@LearningwithLeanne Lol 22 new uploads just as I subscribed, love it ✌

  • @KattTech
    @KattTech Рік тому

    thank you for this video.

  • @Therians4ever761
    @Therians4ever761 Рік тому

    Are you in the hospital?😢😢😢