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.
A fast-transpose is a computer algorithm that quickly transposes a sparse matrix using a relatively small amount of memory. Using arrays normally to record a sparse matrix uses up a lot of memory since many of the matrix's values are zero. In addition, using the normal transpose algorithm to transpose this matrix will take O(cols*elements) amount of time. The fast-transpose algorithm only uses a little memory to record the matrix and takes only O(cols+elements) amount of time, which is efficient considering the number of elements equals cols*rows.
yes, it is true that the transpose of the transpose of a matrix is the original matrix
Algorithm: transpose Input: a matrix M[x][y] Output: the transpose of M (a matrix of order y * x) allocate N[y][x] for r = 0 to x-1 // iterate over rows for c = 0 to y-1 // iterate over columns N[c][r] = M[r][c] next c next r return N
draw the flowchart for transpose of a matrice
The Transpose of a MatrixThe matrix of order n x m obtained by interchanging the rows and columns of the m X n matrix, A, is called the transpose of A and is denoted by A' or AT.
a square matrix that is equal to its transpose
Another sparse matrix.
Invert rows and columns to get the transpose of a matrix
The transpose of a matrix A is the matrix B that is obtained by swapping the rows and columns of A into the columns and rows of B. In algebraic form, if A = {aij} then B = {aji} is its transpose, where 1 ≤ i ≤ n and 1 ≤ j ≤ m.
The classical adjoint of a square matrix A the transpose of the matrix who (i, j) entry is the a i j cofactor.
Hermitian matrix (please note spelling): a square matrix with complex elements that is equal to its conjugate transpose.
It need not be, so the question makes no sense!