TOPICS
Search

Conjugate Matrix


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

 (a_(ij))^_=(a^__(ij)).

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

Using a matrix X in a similarity transformation X^(-1)AX of a given matrix A is also known as conjugating A by X. In this case, B=X^(-1)AX and A are known as similar matrices.


See also

Complex Conjugate, Conjugate Transpose, Similar Matrices, Similarity Transformation

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Conjugate Matrix

Cite this as:

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

Subject classifications