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Proofs of matrix norm properties

Equality occurs when A and B share a support vector. [Pg.34]

It is also possible for other measures of matrix size to be defined, and they are also called norms provided that they satisfy this additional property as well as the three above. [Pg.35]

All the above applies to matrices which are not square, but if a matrix A is square, then because, if V is an eigencolumn of the matrix, we know that AV = XV, any eigenvalue gives a lower bound for any of the norms. [Pg.35]

Clearly the magnitude of the largest eigenvalue is a tighter lower bound than smaller ones. [Pg.35]

It is equally true that any norm is an upper bound for the largest eigenvalue. [Pg.35]


See other pages where Proofs of matrix norm properties is mentioned: [Pg.34]   


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