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Jason Stratos Papadopoulos, blocked in-place transpose of square matrices, in C, sci.math.num-analysis newsgroup (April 7, 1998). See "Source code" links in the references section above, for additional code to perform in-place transposes of both square and non-square matrices. libmarshal Blocked in-place transpose of rectangular matrices for ...
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations). [1] The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [2]
The conjugate transpose of a matrix with real entries reduces to the transpose of , as the conjugate of a real number is the number itself. The conjugate transpose can be motivated by noting that complex numbers can be usefully represented by 2 × 2 {\displaystyle 2\times 2} real matrices, obeying matrix addition and multiplication: [ 3 ]
In Matlab/GNU Octave a matrix A can be vectorized by A(:). GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Julia has the vec(A) function as well.
In [5] are given as examples code of a Matlab functions that creates and matrices for vector of size n = 2, 4, or, 8. Stay open question is it possible to create T r s {\displaystyle Trs} matrices of size, greater than 8.
For matrices in mathematical notation, the first index indicates the row, and the second indicates the column, e.g., given a matrix , the entry , is in its first row and second column. This convention is carried over to the syntax in programming languages, [ 2 ] although often with indexes starting at 0 instead of 1.
In mathematics, especially in linear algebra and matrix theory, the commutation matrix is used for transforming the vectorized form of a matrix into the vectorized form of its transpose. Specifically, the commutation matrix K (m,n) is the nm × mn permutation matrix which, for any m × n matrix A, transforms vec(A) into vec(A T): K (m,n) vec(A ...
Let H be a Hadamard matrix of order n.The transpose of H is closely related to its inverse.In fact: = where I n is the n × n identity matrix and H T is the transpose of H.To see that this is true, notice that the rows of H are all orthogonal vectors over the field of real numbers and each have length .