Definition:Hadamard Matrix/Definition 2
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Definition
A Hadamard matrix $H$ is a square matrix such that:
- $(1): \quad$ all the entries of $H$ are either $+1$ or $-1$
- $(2): \quad H H^\intercal = n \mathbf I_n$
where:
- $H^\intercal$ denotes the transpose of $H$
- $\mathbf I_n$ denotes the identity matrix of order $n$
given that the order of $H$ is $n$.
Also see
- Results about Hadamard matrices can be found here.
Source of Name
This entry was named for Jacques Salomon Hadamard.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Hadamard matrix
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hadamard matrix
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hadamard matrix