transpose(Matrix mat,int rows, int cols ){ //construction step Matrix tmat; for(int i=0;i<rows;i++){ for(int j=0;j<cols;j++){ tmat[j][i] = mat[i][j]; } } }
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yes, it is true that the transpose of the transpose of a matrix is the original matrix
Another sparse matrix.
Hermitian matrix (please note spelling): a square matrix with complex elements that is equal to its conjugate transpose.
It is the conjugate transpose of the matrix. Of course the conjugate parts only matters with complex entries. So here is a definition:A unitary matrix is a square matrix U whose entries are complex numbers and whose inverse is equal to its conjugate transpose U*. This means thatU*U = UU* = I. Where I is the identity matrix.
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.