We saw in Theorem CINM that if a square matrix \(A\) is nonsingular, then there is a matrix \(B\) so that \(AB=I_n\text{.}\) In other words, \(B\) is halfway to being an inverse of \(A\text{.}\) We will see in this section that \(B\) automatically fulfills the second condition (\(BA=I_n\)). Example MWIAA showed us that the coefficient matrix from Archetype A had no inverse. Not coincidentally, this coefficient matrix is singular. We will make all these connections precise now. Not many examples or definitions in this section, just theorems.

- License
- GFDL-1.2
- Submitted At
- September 11th, 2017
- 5 years ago
- Views
- 3
- Type
- Language
- English
- Content Type
- text/html

##### math.la.t.mat.unitary.innerproduct