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GeezerVison is showing mathworld.wolfram.com — Equivalent Matrix -- from Wolfram MathWorld

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Equivalent Matrix

Two matrices A and B are equal to each other, written A=B, if they have the same dimensions m×n and the same elements a_(ij)=b_(ij) for i=1, ..., n and j=1, ..., m.

Gradshteyn and Ryzhik (2000) call an m×n matrix A "equivalent" to another m×n matrix B iff

B=PAQ

for P and Q any suitable nonsingular m×m and n×n matrices, respectively.

See also

Matrix

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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. 1103, 2000.

Referenced on Wolfram|Alpha

Equivalent Matrix

Cite this as:

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

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