# Definition of an upper triangular matrix

math.la.d.mat.triangular.upper

# 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.

##### math.la.d.mat.triangular.upper
GFDL-1.2
Submitted At
September 11th, 2017
6 years ago
Views
2
Type
Textbook
Language
English
Content Type
text/html

# 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.

##### math.la.d.mat.triangular.upper
GFDL-1.2
Submitted At
September 11th, 2017
6 years ago
Views
3
Type
Textbook
Language
English
Content Type
text/html