Definition

Noun: A nonsingular matrix is a square matrix (a matrix with the same number of rows and columns) that has a non-zero determinant. This property makes it invertible, meaning there exists another matrix (its inverse) which, when multiplied with the original, yields the identity matrix.

Usage

The term is used in linear algebra to describe a matrix that is not singular. A singular matrix has a determinant of zero and does not have an inverse. * The system of linear equations has a unique solution because the coefficient matrix is a nonsingular matrix. * To find the inverse, you must first verify that you are dealing with a nonsingular matrix.

Advanced Usage

• Mathematical Context: In theoretical and applied mathematics, a nonsingular matrix is crucial because it represents a linear transformation that is one-to-one and onto. Its columns (and rows) are linearly independent.
• Synonym in Use: The term invertible matrix is often used interchangeably with "nonsingular matrix."

Variants and Related Words

• Singular Matrix (noun): The direct antonym; a square matrix whose determinant is zero and which is not invertible.
• Determinant (noun): A scalar value that can be computed from the elements of a square matrix. The property of being nonsingular is determined by this value.
• Inverse Matrix (noun): The matrix that, when multiplied by the original nonsingular matrix, results in the identity matrix.

Synonyms

• Invertible matrix
• Non-degenerate matrix
• Regular matrix

Antonyms

• Singular matrix
• Degenerate matrix
• Non-invertible matrix

Noun

1. a square matrix whose determinant is not zero