orthogonal diagonalization
Work in Progress
Summary
Spectral theorem, symmetry
Eigenspaces are orthogonal
Equivalent statements for orthogonal diagonalizability
Shortcut for the determinant of symmetric matrices, using submatrices
Concept
Orthogonal diagonalization
- breaking up a complex transformation into a rotation, scale and then reverse rotation
is a rotation matrix
Spectral theorem
the converse is out of scope for MA1522
Orthogonality of eigenspaces
- for symmetric matrices
only perform Gram-Schmidt for vectors within each eigenspace, the eigenspaces are already orthogonal