So I am trying to determine if the difference of two matrices is positive(negative) semi-definite. The matrices, we will call them and , are partitioned as
My problem is that I wish to determine the definiteness of the matrix or/and . These matrices are given by
We know from simple linear algebra that a matrix is positive(negative) semi-definite if and only if all of its principle minors are non-negative(non-positive). With this I have two questions: 1) Does the same hold true for block matrices? 2) If this does hold true the second principle minor, in block form, for both matrices is , what does this mean exactly. Does this mean that the matrices are non-definite?