Math 2.0

definition

Square matrix

Definition

Let RR be a ring and let n≥0n \ge 0 be an integer. A square matrix of order nn over RR is an n×nn \times n matrix over RR. Its main diagonal is the list of the entries a11,a22,…,anna_{11}, a_{22}, \dots, a_{nn}. The set of square matrices of order nn over RR is written Mn(R)M_n(R).

Remarks

The product of two n×nn \times n matrices is again an n×nn \times n matrix, so Mn(R)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.

Explanations

L1 human

A square matrix has as many rows as columns, like a 3×33 \times 3 table. Only square matrices can be multiplied by themselves, so only they have powers like A2A^2. Many important notions, such as the determinant, apply only to square matrices.

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Sources

  1. Web https://en.wikipedia.org/wiki/Square_matrix, lead section

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