Operator Norm
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the operator norm is a means to measure the "size" of certain linear operators. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.Every real m-by-n matrix yields a linear map from Rn to Rm. One can put several different norms on these spaces, as explained in the article on norms. Each such choice of norms gives rise to an operator norm and therefore yields a norm on the space of all m-by-n ma...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the operator norm is a means to measure the "size" of certain linear operators. Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.Every real m-by-n matrix yields a linear map from Rn to Rm. One can put several different norms on these spaces, as explained in the article on norms. Each such choice of norms gives rise to an operator norm and therefore yields a norm on the space of all m-by-n matrices. Examples can be found in the article on matrix norms. If we specifically choose the Euclidean norm on both Rn and Rm, then we obtain the matrix norm which to a given matrix A assigns the square root of the largest eigenvalue of the matrix A A (where A denotes the conjugate transpose of A). This is equivalent to assigning the largest singular value of A.
