Symmetric Matrices and Eigenvectors

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Related lectures (26)

Page 2 of 3

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Diagonalization: Eigenvectors and Eigenvalues

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Spectral Decomposition of Symmetric Matrices

Explores the spectral decomposition of symmetric matrices, including diagonalization and orthogonal basis change matrices.

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Diagonalization: Criteria and Examples

Covers the criteria for diagonalizing a matrix and provides illustrative examples.

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.