Tool to calculate the complex conjugate matrix. The complex conjugate of a matrix M is a matrix denoted $ \overline{M} $ composed of the complex conjugate values of each element.

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For the matrix $ M=[a_{ij}] $, the conjugate matrix is noted with a bar $ \overline{M} $ or with an asterisk $ M^{*} $. For a complex value $ z $, its conjugated value is written $ \overline{z} $ or $ z^{*} $. By generalizing, the formula for calculating the conjugate matrix is:

Use the character i to represent $ i $ the imaginary unit for complex numbers.

What are the properties of a conjugate matrix?

A double conjugated matrix (conjugated two times) is equal to the original matrix. $$ \overline{\overline{M}}=M $$

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