NONSINGULAR MATRIX Meaning and
Definition
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A nonsingular matrix, also referred to as an invertible matrix or non-degenerate matrix, is a concept in linear algebra that describes a square matrix that possesses an inverse.
In a more detailed explanation, a nonsingular matrix is a square matrix of order n, which means that it has the same number of rows and columns. It is non-degenerate, which implies that its determinant, a scalar value associated with the matrix, is not equal to zero. The determinant essentially describes the "volume" of a matrix and signifies whether the system of linear equations represented by the matrix has a unique solution. A nonzero determinant indicates that the matrix is nonsingular, meaning that its rows and columns are linearly independent.
The property of being nonsingular is closely connected to the existence of an inverse matrix. An inverse matrix is a matrix that, when multiplied with the original matrix, yields the identity matrix. The identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. For instance, if matrix A is nonsingular, it has an inverse denoted by A^(-1). When A is multiplied by its inverse A^(-1), the result is the identity matrix, I. This property makes nonsingular matrices valuable in solving systems of linear equations, as they allow for straightforward calculation of unique solutions using matrix algebra methods.
In summary, a nonsingular matrix is a square matrix that is invertible, possessing a nonzero determinant and an inverse that can be multiplied with the original matrix to yield the identity matrix.
Common Misspellings for NONSINGULAR MATRIX
- bonsingular matrix
- monsingular matrix
- jonsingular matrix
- honsingular matrix
- ninsingular matrix
- nknsingular matrix
- nlnsingular matrix
- npnsingular matrix
- n0nsingular matrix
- n9nsingular matrix
- nobsingular matrix
- nomsingular matrix
- nojsingular matrix
- nohsingular matrix
- nonaingular matrix
- nonzingular matrix
- nonxingular matrix
- nondingular matrix
- noneingular matrix
Etymology of NONSINGULAR MATRIX
The word "nonsingular" is derived from the combination of the prefix "non-" meaning "not" or "lacking" and the word "singular".
The term "singular" in mathematics refers to a matrix that does not possess an inverse or determinant equal to zero. In contrast, a nonsingular matrix is one that has an inverse, which means it has nonzero determinants.
Therefore, the word "nonsingular" was coined to describe matrices that lack singularity or non-invertibility.
