advanced-linear-algebra

The real spectral theorem

taught

A real operator is self-adjoint if and only if it's orthogonally diagonalizable -- Linear Algebra I's symmetric-matrix fact, generalized from matrices to operators and reproved from the adjoint.

Taught in

The real spectral theorem
Advanced Linear Algebra

Requires

self-adjoint-operators-and-real-eigenvalues required
symmetric-matrices-and-orthogonal-diagonalization required

Required by

Conics, quadrics, and the principal-axis theorem required
SVD versus eigendecomposition required

Local knowledge map

Click to expand

Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.