https://www.youtube.com/watch?v=mhy-ZKSARxI
Symmetric
Recall: If P is an orthogonal n × n matrix, then P −1 = P T , which implies A = PDP^T is diagonalizable and symmetric.
Spectral Thm
An n × n symmetric matrix A has the following properties.
- All eigenvalues of A are real.
- The dimenison of each eigenspace is full, that it’s dimension is equal to it’s algebraic multiplicity.
- The eigenspaces are mutually orthogonal.
- A can be diagonalized: A = PDP^T , where D is diagonal and P is orthogonal.
Spectal Decomp
