Convexity and unique minimum when matrices are the parameter


How does the concept of convexity and conditions unique minimum extend to functions that depend on matrices (ex; matrix factorization ,K means). I understand the definition for f: R^D--> R but not sure what is the mathematical definition of convexity for f: R^2 x R^2--> R. of f: R^(NxM)--> R

thanks for the help

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