# Permutation Matrix

In mathematics, in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry 1 in each row and each column and 0s elsewhere. Each such matrix represents a specific permutation of m elements and, when used to multiply another matrix, can produce that permutation in the rows or columns of the other matrix.

### Other articles related to "permutations, permutation matrix, matrix, permutation":

Cauchy–Binet Formula - Proof
... increasing bijection → S, and π,σ the permutations of such that and then is the permutation matrix for π, is the permutation matrix for σ, and LfRg is the permutation matrix for, and since the ... use just one of them, say the former, and use that a matrix product LfB either consists of a permutation of the rows of Bf, (if f is injective), or has at least ...
Permutation Matrix - Properties
... Given two permutations π and σ of m elements and the corresponding permutation matrices Pπ and Pσ This somewhat unfortunate rule is a consequence of the ... As permutation matrices are orthogonal matrices (i.e ... the inverse matrix exists and can be written as Multiplying times a column vector g will permute the rows of the vector Now applying after applying gives the same result as ...
The Art Of Fugue - The Unfinished Fugue - The Permutation Matrix
... of Bach's oeuvre occurring mainly in the vocal fugues that of the permutation fugue ... of the first three subjects he "programmed" the later permutation stretti, then applied the expositions as "programs", "algorithms" ... The permutation matrix, apart from originating authentically with Bach, can be proved to have been ready at the time of the genesis of the work (that is, earlier than the ...

### Famous quotes containing the word matrix:

As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.
Margaret Atwood (b. 1939)