qProperties of Matrix Norm:
q Frobenius norm
•
•
• Let A and B be any matrices with
appropriate dimensions. Then
• 1. r(A) £ ||A|| (This is also true
for F norm and any induced
matrix norm).
• 2. ||AB||£ ||A|| ||B||. In particular, this gives ||A-1|| ³ ||A||-1 if A is invertible. (This is also true for any induced
matrix norm.)
• 3. ||UAV||=||A|| and ||UAV||F=||A||F, for any appropriately
dimensioned unitary matrices U
and V.
• 4. ||AB||F £ ||A|| ||B||F, and ||AB||F £ ||B|| ||A||F