Nonsingular意思

"Nonsingular" is a term that is used in various fields, such as mathematics, physics, and engineering, to indicate that something is not singular. The meaning of "singular" can vary depending on the context, but it often implies that something is exceptional, abnormal, or has some sort of special property that sets it apart from the rest.

In mathematics, a nonsingular point on a curve or surface is one that is not a point of self-intersection, cusp, or other type of singularity. For example, a nonsingular point on a curve in the plane is one where the curve has a well-defined tangent line.

In linear algebra, a nonsingular matrix is one that is invertible, meaning that it has a inverse matrix that "undoes" the operations performed by the original matrix. A singular matrix, on the other hand, is one that does not have an inverse, often because it is not full rank.

In differential geometry, a nonsingular point on a manifold is one where the tangent space has a well-defined dimension, and the manifold is smooth at that point.

In control theory, a nonsingular system is one that is stable and has full rank, meaning that it can be controlled and observed effectively.

In general, the term "nonsingular" is used to indicate that something is normal, well-behaved, and does not have any of the special or problematic properties associated with singularities.