HadamardMatrix
returns an n×n Hadamard matrix.
Details and Options

- Each entry Hrs of the Hadamard matrix is by default defined as
, where
,
is the
bit in the binary representation of the integer
, and
.
must be a power of two.
- Rows or columns of the HadamardMatrix are basis sequences of the DiscreteHadamardTransform.
- The Hadamard matrix is symmetric and orthogonal and is thus its own inverse. »
- The following options are supported:
-
Method Automatic specify the sequency ordering method WorkingPrecision ∞ precision at which to create entries
Examples
open allclose allOptions (2)
Properties & Relations (3)
The discrete Hadamard transform of a vector is equivalent to multiplying the vector by the Hadamard matrix:
Sylvester's construction of a Hadamard matrix of order 4:
This corresponds to the bit complement sequency ordering:
The Hadamard matrix is symmetric and orthogonal:
Because of these properties, the Hadamard matrix is its own inverse:
Text
Wolfram Research (2012), HadamardMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/HadamardMatrix.html (updated 2023).
CMS
Wolfram Language. 2012. "HadamardMatrix." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/HadamardMatrix.html.
APA
Wolfram Language. (2012). HadamardMatrix. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/HadamardMatrix.html