Square matrix

Definition

A square matrix is a matrix with an equal number of rows and columns. It is often used in solving systems of linear equations and performing matrix operations.

5 Must Know Facts For Your Next Test

1. A square matrix has the same number of rows and columns, denoted as $n \times n$.
2. The determinant of a square matrix is crucial for determining whether the system has a unique solution in Cramer's Rule.
3. An identity matrix is a special type of square matrix where all diagonal elements are 1 and all other elements are 0.
4. The inverse of a square matrix, if it exists, can be used to solve systems of equations via the equation $A^{-1}Ax = A^{-1}b$.
5. In eigenvalue problems, only square matrices have eigenvalues and eigenvectors.

Review Questions

Related terms

Determinant:

A scalar value that can be computed from the elements of a square matrix and determines whether the matrix has an inverse.

Identity Matrix:

A special type of square matrix with ones on the diagonal and zeros elsewhere, denoted as $I_n$ for an $n \times n$ identity matrix.

Inverse Matrix:

A square matrix $A^{-1}$ that, when multiplied by its original matrix $A$, yields the identity matrix: $AA^{-1} = I$.