Congratulations for your appointment as Public Engagement Lead and a Departmental Lecturer at the department of continuing education in University of Oxford. We have an Oxford Mathematics Lecturer here people!
In the last example, the two vectors only vectors are a basis of polynomials with degree less than or equal to 2. But let's say our vector space was polynomials with degree less than or equal to 3, and we were only given 2 linearly independent vectors, is there a way to construct an orthonormal basis? (ie. extend the orthonormal set with 2 vectors which you found into a set with 3 vectors)
Hey I reckon you should take a look at the Australian HSC math exams. There's 3 different "hard" ones. Advanced, ext 1 and ext 2. You may just have to brush up on the calculator
Here you show that, given an inner product and a linear independent set we can always create an orthonormal set. Can we go the other way? Can we take a linearly independent set, set it to be orthonormal, and always find an inner product that satisfies this?
What are the reasons for take\int xf(x)g(x)dx as inner product in your last example? Is possible to do G-S process fir a two dimensional space? thanks for your videos
I think it's just a way to define the inner product in that question. It doesn't break any of the properties needed for it to be an inner product, so, it's valid.
hello, im sorry if i dont grasp it yet, but isnt the example in the polynomial space not an inner space? shoulnt there be absolute values? if i take g(x) = -x, f(x) = x, then i have the integral of -x^3, which amounts to a negative value? Am I right? or what am I missing? Thank you for your help
Isn't Gram-Schmidt process that somehow very intuitively understandable process of turning any basis of an Euclidean space into an ortnonormal basis? I never thought it even had a name because it seems so straightforward.
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Congratulations for your appointment as Public Engagement Lead and a Departmental Lecturer at the department of continuing education in University of Oxford. We have an Oxford Mathematics Lecturer here people!
We just covered this in my undergraduate linear algebra class!
Great work professor!
In the last example, the two vectors only vectors are a basis of polynomials with degree less than or equal to 2. But let's say our vector space was polynomials with degree less than or equal to 3, and we were only given 2 linearly independent vectors, is there a way to construct an orthonormal basis? (ie. extend the orthonormal set with 2 vectors which you found into a set with 3 vectors)
Hey I reckon you should take a look at the Australian HSC math exams. There's 3 different "hard" ones. Advanced, ext 1 and ext 2. You may just have to brush up on the calculator
Thanks for bringing higher math to the "masses" 🙂
Here you show that, given an inner product and a linear independent set we can always create an orthonormal set. Can we go the other way? Can we take a linearly independent set, set it to be orthonormal, and always find an inner product that satisfies this?
At 16:21 is there a difference between the x written like 2 c's and the x written with straight lines?
No, they're exactly the same
What are the reasons for take\int xf(x)g(x)dx as inner product in your last example? Is possible to do G-S process fir a two dimensional space? thanks for your videos
I think it's just a way to define the inner product in that question. It doesn't break any of the properties needed for it to be an inner product, so, it's valid.
hello, im sorry if i dont grasp it yet, but isnt the example in the polynomial space not an inner space? shoulnt there be absolute values? if i take g(x) = -x, f(x) = x, then i have the integral of -x^3, which amounts to a negative value? Am I right? or what am I missing? Thank you for your help
I'm far too dumb to watch this or else i would ... Maybe if i don't have headache or my mother hounding me if i don't get off screen. Love you lots!
Nah…. You could do it. You just have to work up the this point.
Isn't Gram-Schmidt process that somehow very intuitively understandable process of turning any basis of an Euclidean space into an ortnonormal basis? I never thought it even had a name because it seems so straightforward.
Orthonormal basis yes
Please do modified graham schmidt
🐐🔥
Hi tom
Hi can you please react to jee advanced math paper. It is very tough. It is an exam given by highschool students to get into respectable colleges IIT
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Yo I have that shirt
Hlo, give answer of this question.
Number of tangents of curve y=e^|x| at (0, 1),
Options are
a) 2, b) 4, c) 1,d) 0
Do you have any maths videos for normal people, who are not oxbridge educated?
Dude this is for normal people, it’s just linear algebra