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Diagonalization

via YouTube

Overview

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This course develops diagonalization through eigenvalues and eigenvectors, including tests for diagonalizability, pseudo-diagonalization, simultaneous diagonalization, and matrix square roots. It also connects these ideas to differential systems, matrix limits, Markov chains, and the Cayley–Hamilton theorem.

Syllabus

Eigenvalues and Eigenvectors.
Oh shift !.
Eigenvectors and linear independence.
Diagonalize 2x2 matrix.
Diagonalization and Legend of Zelda.
Pseudo diagonalization.
Eigenvectors and Geometry.
Diagonalizability.
Derivative diagonalizable ?.
Ultimate diagonalization test.
Non diagonalization test.
Direct Sum.
Not diagonalizable.
Square root of a matrix.
System of differential equations.
Matrix Limits and Markov Chains.
Matrix Limit Gone Wrong.
Neat determinant.
Cayley Hamilton Theorem.
Simultaneous Diagonalization.
matrix choose a matrix.

Taught by

Dr Peyam

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