Square Matrix

Tags: #◇CSMATH2 #◇Linear Algebra #◇Computational Mathematics #◇Matrices #◇Matrix Operations #◇Square Matrix #◇Computer Science #◇Vector Spaces #◇Linear Transformations

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◇Overview

Main Diagonal and Trace of a Matrix

◇Details / Theory

◇◇Special Types of Square Matrices

◇Main Diagonal and ◇Trace of a Matrix

◇Specific Types of Square Matrices

◇Diagonal Matrix #### ◇Scalar Matrix #### ◇Identity Matrix (In​) #### ◇Triangular Matrices #### ◇Symmetric Matrix #### ◇Skew-Symmetric Matrix

◇◇Powers of a Matrix

◇◇Polynomial in a Matrix

◇◇Important Remarks on ◇Matrix Multiplication

◇◇Inverse of a Matrix

◇◇Elementary Matrices

◇Common Pitfalls

Not all square matrices are invertible — only those with $\det(A) \neq 0$. Operations like determinant, trace, and eigenvalues only apply to square matrices.

◇Summary

TL;DR — A square matrix has equal rows and columns ($n \times n$). Only square matrices can have determinants, inverses, eigenvalues, and traces.

◇Links

Related: - ◇Special Types of Square Matrices - ◇Main Diagonal - ◇Trace of a Matrix - ◇Diagonal Matrix - ◇Scalar Matrix - ◇Identity Matrix - ◇Triangular Matrices - ◇Symmetric Matrix - ◇Skew-Symmetric Matrix - ◇Powers of a Matrix - ◇Polynomial in a Matrix - ◇Important Remarks - ◇Matrix Multiplication - ◇Inverse of a Matrix - ◇Elementary Matrices Source / Reference:

◇References & Navigation

• Previous Topic: ◇Special Types of Square Matrices
• Next Topic: ◇Symmetric Matrix
• Related Notes: ◇Elementary Row Operation, ◇Symmetric Matrix, ◇Matrices Detailed