Definition:Hadamard Matrix/Definition 2

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

• Equivalence of Definitions of Hadamard Matrix

• 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