What's the conjugate of a matrix function?

88 Views Asked by At

As we all know, the conjugate of a function for a vector $\textbf{x}$ is $$ f^*(\textbf{y})=sup(\textbf{y}^T\textbf{x}-f(\textbf{x})) $$ what's the conjugate of a function for a matrix $\textbf{X}$? what's the $f^*(\textbf{Y})$?