Principal Axes Theorem

Related lectures (26)

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Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Introduces orthogonal and symmetric matrices in linear algebra with practical examples.

Explores Sylvester's Inertia Theorem, relating eigenvalues to diagonal entries in symmetric matrices.

Covers the decomposition of matrices into triangular blocks and spectral decomposition.

Delves into singular value decomposition and its applications in linear algebra.

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

Explores diagonalization of symmetric matrices and their eigenvalues, emphasizing orthogonal properties.

Explores orthogonal base change in linear algebra, focusing on matrices and transformations.

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

Covers the process of finding orthogonal bases and spectral decomposition of symmetric matrices.