NONSINGULAR Meaning and
Definition
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Nonsingular, an adjective often used in mathematics and linear algebra, refers to a property of a square matrix that possesses a unique inverse or determinant equal to zero. When a square matrix is nonsingular, it means that it is invertible, which allows the existence of an inverse matrix that can be multiplied with the original matrix to yield the identity matrix. Additionally, for a matrix to be nonsingular, it must not have any zero eigenvalues, indicating that it can be inverted without any issues.
In linear algebra, the inverse of a nonsingular matrix plays a crucial role in solving systems of linear equations. When the coefficient matrix of a system is nonsingular, it means that there is a unique solution to the system of equations, as the inverse matrix allows for the direct calculation of the solution vector.
The property of being nonsingular is often contrasted with the concept of singularity. A singular matrix, as opposed to a nonsingular matrix, lacks an inverse or possesses a determinant equal to zero. Consequently, when dealing with singular matrices, it becomes impossible to find a unique solution for a system of linear equations involving the matrix coefficients.
In summary, the term nonsingular describes a square matrix that possesses a unique inverse, allowing the determination of a unique solution for systems of linear equations.
Etymology of NONSINGULAR
The word "nonsingular" is derived from the combination of the prefix "non-" which means "not" or "without", and the word "singular".
The root word "singular" comes from the Latin word "singularis", which means "single", "unique", or "remarkable". In English, "singular" refers to something that is extraordinary, outstanding, or exceptional.
By adding the prefix "non-" to "singular", the word "nonsingular" is formed, defining something that is not extraordinary or exceptional. It indicates that a particular object, concept, or mathematical entity is not singular in nature.
