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Compatible


The matrix norm ||A|| associated with a matrix A and the vector norm |x| associated with a vector x are compatible if the product Ax is defined and

 ||Ax||<=||A|||x|.

Thus, ||A|| and |x| satisfy this compatibility inequality.


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References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 2000, 1980.

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Compatible

Cite this as:

Weisstein, Eric W. "Compatible." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Compatible.html

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