# Hadamard transform

## Involutive change of basis in linear algebra / From Wikipedia, the free encyclopedia

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The **Hadamard transform** (also known as the **Walsh–Hadamard transform**, **Hadamard–Rademacher–Walsh transform**, **Walsh transform**, or **Walsh–Fourier transform**) is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric, involutive, linear operation on 2^{m} real numbers (or complex, or hypercomplex numbers, although the Hadamard matrices themselves are purely real).

The Hadamard transform can be regarded as being built out of size-2 discrete Fourier transforms (DFTs), and is in fact equivalent to a multidimensional DFT of size 2 × 2 × ⋯ × 2 × 2.[2] It decomposes an arbitrary input vector into a superposition of Walsh functions.

The transform is named for the French mathematician Jacques Hadamard (French: [adamaʁ]), the German-American mathematician Hans Rademacher, and the American mathematician Joseph L. Walsh.