Thank you so much! I've been studying linear algebra to understand my quantum mechanics modules better, so this is perfect timing for me. 😊 Much appreciated!
Fact that similar matrices have the same eigenvalues is used in numerical linear algebra to find eigenvalues There are used transformations which preserve similarity like Householder reflections or Givens rorations or just modification of Gaussian elimination To preserve similarity we must perform elementary operations on both rows and columns
Why is lambda the same on both sides? The characteristic polonomial has some value lambda, but it doesnt need to be the same value for all matrices. Using the same lambda on both sides seems to assume the matrices have the same characteristic. I would think that needs to be proven.
It's easy to show that if A and B are similar then (A - λI) and (B - λI) are similar. Next use the fact that similarity preserves the determinant. That's it.
The characteristic of a Prime Newtons video is that it is chock full of useful information about math similar to the best teachers on UA-cam. 😢😊
This went SO far over my head that I need a telescope!!
Thank you so much! I've been studying linear algebra to understand my quantum mechanics modules better, so this is perfect timing for me. 😊 Much appreciated!
Fact that similar matrices have the same eigenvalues is used in numerical linear algebra to find eigenvalues
There are used transformations which preserve similarity like Householder reflections or Givens rorations or just modification of Gaussian elimination
To preserve similarity we must perform elementary operations on both rows and columns
I love this guy,I mean his teaching style and the way he acts 😊😊
What does drawing the square in the end mean?
Proof is complete
@@PrimeNewtons thank you
Why is lambda the same on both sides? The characteristic polonomial has some value lambda, but it doesnt need to be the same value for all matrices. Using the same lambda on both sides seems to assume the matrices have the same characteristic. I would think that needs to be proven.
Here are 235 chapters of mathematics:🤫🗣️
1. Arithmetic Operations
2. Properties of Numbers
3. Fractions and Decimals
4. Integers
5. Prime Numbers
6. Factors and Multiples
7. Divisibility Rules
8. Exponents and Powers
9. Order of Operations
10. Number Patterns and Sequences
11. Place Value
12. Roman Numerals
13. Ratio and Proportion
14. Percentages
15. Profit and Loss
16. Simple Interest
17. Compound Interest
18. Discount and Markup
19. Average
20. Mean, Median, and Mode
21. Range
22. Probability
23. Counting Techniques
24. Permutations and Combinations
25. Sets
26. Union and Intersection of Sets
27. Subsets and Power Sets
28. Venn Diagrams
29. Functions and Relations
30. Domain and Range
31. Function Notation
32. Graphs of Functions
33. Inverse Functions
34. Linear Functions
35. Quadratic Functions
36. Polynomial Functions
37. Rational Functions
38. Exponential Functions
39. Logarithmic Functions
40. Trigonometric Functions
41. Trigonometric Identities
42. Trigonometric Equations
43. Law of Sines
44. Law of Cosines
45. Right Triangle Trigonometry
46. Graphs of Trigonometric Functions
47. Polar Coordinates
48. Parametric Equations
49. Sequences and Series
50. Arithmetic Sequences and Series
51. Geometric Sequences and Series
52. Binomial Theorem
53. Mathematical Induction
54. Complex Numbers
55. Arithmetic Operations with Complex Numbers
56. Polar Form of Complex Numbers
57. De Moivre's Theorem
58. Matrices
59. Matrix Operations
60. Determinants
61. Inverse of a Matrix
62. Systems of Linear Equations
63. Gauss-Jordan Elimination
64. Cramer's Rule
65. Vector Spaces
66. Linear Independence and Dependence
67. Basis and Dimension
68. Inner Product Spaces
69. Eigenvalues and Eigenvectors
70. Diagonalization
71. Orthogonalization
72. Differential Calculus
73. Limits and Continuity
74. Derivatives
75. Differentiation Rules
76. Implicit Differentiation
77. Related Rates
78. Higher Order Derivatives
79. Mean Value Theorem
80. L'Hôpital's Rule
81. Taylor and Maclaurin Series
82. Integral Calculus
83. Indefinite Integrals
84. Integration by Substitution
85. Integration by Parts
86. Trigonometric Integrals
87. Partial Fractions
88. Improper Integrals
89. Applications of Integration
90. Area Under a Curve
91. Volume of Revolution
92. Arc Length and Surface Area
93. Polar Coordinates
94. Parametric Equations
95. Differential Equations
96. First Order Differential Equations
97. Second Order Differential Equations
98. Homogeneous Differential Equations
99. Nonhomogeneous Differential Equations
100. Systems of Differential Equations
101. Permutations and Combinations
102. Fourier Series
103. Partial Differential Equations
104. Vector Calculus
105. Vector Fields
106. Line Integrals
107. Green's Theorem
108. Divergence Theorem
109. Stoke's Theorem
110. Conservative Vector Fields
111. Gradient, Divergence, and Curl
112. Three-Dimensional Coordinate Systems
113. Parametric Surfaces
114. Cylindrical and Spherical Coordinates
115. Multivariable Calculus
116. Partial Derivatives
117. Chain Rule
118. Directional Derivatives
119. Gradient Vector
120. Tangent Planes and Normal Vectors
121. Double Integrals
122. Triple Integrals
123. Change of Variables in Multiple Integrals
124. Surface Integrals
125. Flux Integrals
126. Vector Analysis
127. Green's, Gauss's, and Stokes's Theorems
128. Complex Analysis
129. Complex Functions
130. Analytic Functions
131. Contour Integration
132. Cauchy's Integral Theorem
133. Residue Theory
134. Laurent Series
135. Conformal Mapping
136. Real Analysis
137. Limits and Continuity
138. Sequences and Series
139. Differentiation and Integration
140. Metric Spaces
141. Topology
142. Functions of Several Variables
143. Continuous Functions
144. Differentiable Functions
145. Riemann Integration
146. Measure Theory
147. Lebesgue Integration
148. Hilbert Spaces
149. Banach Spaces
150. Fourier Analysis
151. Fourier Transform
152. Laplace Transform
153. Z-Transform
154. Convolution
155. Wavelets
156. Distribution Theory
157. Differential Geometry
158. Curves and Surfaces
159. Tangent Spaces and Normal Spaces
160. Riemannian Manifolds
161. Geodesics
162. Gaussian Curvature
163. Differential Forms
164. Exterior Derivative
165. Integration on Manifolds
166. Lie Groups
167. Lie Algebras
168. Lie Theory
169. Algebraic Topology
170. Homotopy Theory
171. Homology Theory
172. Cohomology Theory
173. Fiber Bundles
174. Characteristic Classes
175. Differential Topology
176. Morse Theory
177. Algebraic Geometry
178. Affine Geometry
179. Projective Geometry
180. Conic Sections
181. Algebraic Curves
182. Algebraic Surfaces
183. Commutative Algebra
184. Rings and Ideals
185. Modules
186. Noetherian Rings
187. Field Theory
188. Galois Theory
189. Algebraic Number Theory
190. Arithmetic Geometry
191. Elliptic Curves
192. Diophantine Equations
193. Cryptography
194. Coding Theory
195. Group Theory
196. Group Actions
197. Sylow Theory
198. Solvable and Nilpotent Groups
199. Representation Theory
200. Group Extensions
201. Group Cohomology
202. Commutative Group Theory
203. Algebraic Structures
204. Homological Algebra
205. Category Theory
206. Abstract Algebra
207. Universal Algebra
208. Semigroup Theory
209. Ring Theory
210. Noncommutative Ring Theory
211. Field Theory
212. Lattice Theory
213. Ordered Sets
214. Boolean Algebra
215. Topological Spaces
216. Metric Spaces
217. Continuity and Convergence
218. Compact Spaces
219. Connected Spaces
220. Separation Axioms
221. Product Spaces
222. Quotient Spaces
223. Manifolds
224. Smooth Manifolds
225. Differentiable Manifolds
226. Lie Groups
227. Lie Algebras
228. Lie Theory
229. Fiber Bundles
230. Differential Forms
231. Integration on Manifolds
232. Differential Operators
233. Riemannian Geometry
234. Symplectic Geometry
235. Pythagoras theorem
If you saw this,you gotta subscribe me😉
Plz bro🤝❤️🗿🦅
235. Pythagoras theorem LOL
I would've subscribed if you had all of this content covered on your channel. 😉
Nice
A black man with bright knowledge 👍👏.
Mr Prime is black. So what?
What does that have to do with anything ?
Stop leening stop leaving
It's easy to show that if A and B are similar then (A - λI) and (B - λI) are similar. Next use the fact that similarity preserves the determinant. That's it.
That's essentially what he did, without stating as much.