Largest singular value norm of a matrix
For a matrix , we define the largest singular value (or, LSV) norm of to be the quantity
This quantity satisfies the conditions to be a norm (see here). The reason why this norm is called this way is given here.
The LSV norm can be computed as follows. Let us square the above. We obtain a representation of the squared LSV norm as a Rayleigh quotient of the matrix :
This shows that the squared LSV norm is the largest eigenvalue of the (positive semi-definite) symmetric matrix , which is denoted . That is: