31. The most immediate case is to apply polynomial functions to a square matrix , extending what has just been discussed. 32. Here they are overlaid and each generally has complex entries extending to all four corners of the square matrix . 33. A square matrix has an inverse if and only if its determinant has an inverse in the coefficient ring. 34. Often these are the square matrix rings, but under certain conditions " infinite matrix rings " are also possible. 35. For a square matrix , the trace is the sum of the diagonal elements, hence the sum over a common index. 36. Does anyone know a proof that if A is a square matrix then there's a matrix B s . t. 37. Moreover, any square matrix with zero trace is unitarily equivalent to a square matrix with diagonal consisting of all zeros. 38. If, the Macaulay matrix is the Sylvester matrix, and is a square matrix , but this is no longer true for. 39. Moreover, any square matrix with zero trace is unitarily equivalent to a square matrix with diagonal consisting of all zeros. 40. There are several techniques for lifting a real function to a square matrix function such that interesting properties are maintained.
