For diagonalizable matrices, the trace of a multi-variable matrix function, defined as the sum of f over all eigenvalue tuples, inherits monotonicity and convexity of f.
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Trace of Multi-variable Matrix Functions and its Application to Functions of Graph Spectrum
For diagonalizable matrices, the trace of a multi-variable matrix function, defined as the sum of f over all eigenvalue tuples, inherits monotonicity and convexity of f.