Walsh matrix: Difference between revisions

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A '''Walsh matrix''' is a specific square matrix of dimensions 2''n'', where ''n'' is some particular natural number. The ~~cells~~ of the matrix are either '''+1''' or '''−1''' and its rows as well as columns are orthogonal, ''i.e. dot product is zero''. Each row of a Walsh matrix corresponds to a Walsh function.

A '''Walsh matrix''' is a specific square matrix of dimensions 2''n'', where ''n'' is some particular natural number. The elements of the matrix are either '''+1''' or '''−1''' and its rows as well as columns are orthogonal, ''i.e. dot product is zero''. Each row of a Walsh matrix corresponds to a Walsh function.

Walsh matrices are a special case of Hadamard matrices. The ''naturally ordered'' Hadamard (Walsh) matrix is defined by the recursive formula below, and the ''sequency-ordered'' Hadamard (Walsh) matrix is formed by rearranging the rows so that the number of sign changes in a row is in increasing order.

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;* Write a routine that, given a natural number '''k''', returns a '''naturally ordered''' Walsh matrix of order 2''k''.

;* Display a few sample generated matrices.

::''Traditionally, Walsh matrices use '''1''' & '''-1''' to denote the different cell values in text mode, or '''~~red~~''' and '''~~green~~''' blocks in image mode. You may use whichever display mode is most convenient for your particular language.''

::''Traditionally, Walsh matrices use '''1''' & '''-1''' to denote the different cell values in text mode, or '''green''' and '''red''' blocks in image mode. You may use whichever display mode is most convenient for your particular language.''

;Stretch

;* Also generate '''sequency ordered''' Walsh matrices.

;* Also, optionally generate '''sequency ordered''' Walsh matrices.

::''A sequency ordered Walsh matrix has the rows sorted by number of sign changes.''

;See also

;* [[wp:Walsh_matrix|Wikipedia: Walsh matrix]]

;* [[Kronecker product|Related task: Kronecker product]]