Linear and multilinear algebra; matrix theory Definition

Square matrix

Builds on Matrix

Definition

Let $R$ be a ring and let $n \ge 0$ be an integer. A square matrix of order $n$ over $R$ is an $n \times n$ matrix over $R$ . Its main diagonal is the list of the entries $a_{11}, a_{22}, \dots, a_{nn}$ . The set of square matrices of order $n$ over $R$ is written $M_n(R)$ .

Remarks

The product of two $n \times n$ matrices is again an $n \times n$ matrix, so $M_n(R)$ is a ring. The trace, the determinant and the eigenvalues are defined for square matrices. A square matrix represents a linear map from a space to itself.

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Matrix definition
Square matrix definition

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Tag	`0CP7YY6NAG`
URI	`m2://0CP7YY6NAG`
Kind	definition
Writing	W1 stated
MSC	15A99
Defines	Square matrix
Uses	Matrix

Square matrix

Definition

Remarks

Reading path

Where this leads

Further reading

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