A conjugate matrix is a matrix obtained from a given matrix by taking the complex conjugate of each element of (Courant and Hilbert 1989, p. 9), i.e.,

The notation is sometimes also used, which can lead to confusion since this symbol is also used to denote the conjugate transpose.

Using a matrix in a similarity transformation of a given matrix is also known as conjugating by . In this case, and are known as similar matrices.

See also

Complex Conjugate, Conjugate Transpose, Similar Matrices, Similarity Transformation

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References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 355-356, 1985.Ayres, F. Jr. Schaum's Outline of Theory and Problems of Matrices. New York: Schaum, pp. 12-13, 1962.Courant, R. and Hilbert, D. Methods of Mathematical Physics, Vol. 1. New York: Wiley, 1989.

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Conjugate Matrix

Cite this as:

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

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