There is a simple routine for checking if a matrix is positive definite called the Cholesky decomposition. If the matrix isn't, Cholesky functions instantly return an error saying it is not positive definite.
Is there a similar simple routine for checking if a matrix is concave or convex? trying to avoid the laborious inequality proof-check on paper, as well as visually intersecting a line through the graph of the function.
Matrices I had in mind to check for convexity were the covariance matrix, correlation matrix, and matrices filled with probabilities (histogram-estimated pdf values) of multiple variables along the columns (stochastic matrix I guess is what they're called).