Linear and multilinear algebra; matrix theory Definition

Normal matrix

Definition

Let $A$ be an $n \times n$ complex matrix. The matrix $A$ is normal when $A A^* = A^* A,$ where $A^*$ is the conjugate transpose of $A$ .

Remarks

Hermitian, skew-Hermitian and unitary matrices are normal. A real matrix is normal when $A A^T = A^T A$ ; real symmetric and orthogonal matrices are examples. The matrix $\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}$ is not normal. A matrix is normal if and only if its map on $\C^n$ is a normal operator for the standard inner product.

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Matrix definition
Transpose definition
Conjugate transpose definition
Normal matrix definition

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Tag	`0XYKE8BE7X`
URI	`m2://0XYKE8BE7X`
Kind	definition
Writing	W1 stated
MSC	15B57, 15A21
Defines	Normal matrix
Uses	Conjugate transpose

Normal matrix

Definition

Remarks

Reading path

Where this leads

Further reading

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