About this document
Matrix Norms and Properties Explained by Anna Francesca Marcelo is a document available to read on EtoBox.
The document defines a matrix norm ||A|| for a k x m matrix A as ||A|| = trace(AA^T) where A^T is the transpose of A. It then shows that this matrix norm satisfies the three properties needed to be a valid norm: 1) ||A|| ≥ 0 and ||A|| = 0 if and only if A is the zero matrix, 2) ||cA|| = |c|||A|| for any scalar c, and 3) the triangular inequality ||A + B|| ≤ ||A|| + ||B||. It also shows that ||A|| = ||A^T|| and that for conformable matrices A and B, ||AB|| ≤ ||A||
- Author
- Anna Francesca Marcelo
- Language
- EN