Diagonalization of Linear Transformations

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Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Covers the reduction of a linear transformation in a 2-dimensional space to find a simpler matrix representation.

Covers the diagonalization of matrices with distinct eigenvalues and the importance of this process.

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Covers the method of diagonalization for determining if a non-square matrix A is diagonalizable.