Orthonormal Diagonalization - A First Course in Linear Algebra


We have seen in Section SD that under the right conditions a square matrix is similar to a diagonal matrix. We recognize now, via Theorem SCB, that a similarity transformation is a change of basis on a matrix representation. So we can now discuss the choice of a basis used to build a matrix representation, and decide if some bases are better than others for this purpose. This will be the tone of this section. We will also see that every matrix has a reasonably useful matrix representation, and we will discover a new class of diagonalizable linear transformations. First we need some basic facts about triangular matrices.

License
GFDL-1.2
Submitted At
September 11th, 2017
 3 years ago
Views
2
Type
 Textbook
Language
 English
Content Type
text/html
  • math.la.t.mat.normal.diagonalize

History

September 11th, 2017 3 years ago

Submitted by Jim Fowler