The Transpose of a Matrix
The 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.
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Transpose means swap places. In maths, the term is usually used for matrices. It means truning the matrix around so that its rows become columns and columns become rows.
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
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The trace of a 3 by 3 matrix A is defined as the summation of n=3;i=1;aii.
If A is a 3x4 matrix with values ([a11, a12, a13, a14], [a21, a22, a23, a24], [a31, a32, a33, a34]) then its transpose AT is a 4x3 matrix values with its values changed diagonally like so, ([a11, a21, a31], [a12, a22, a32], [a13, a23, a33], [a14, a24, a34])