Vänstersingulära

Vänstersingulära is a term used in the context of linear algebra and matrix theory, specifically referring to matrices that are singular and have a determinant of zero. A matrix is considered singular if it does not have an inverse, meaning there is no matrix B such that AB = BA = I, where I is the identity matrix and A is the given matrix.

The term "vänstersingulära" translates to "left singular" in English, which is a bit misleading in the context of matrix theory. In linear algebra, the term "singular" is typically used to describe a matrix that is not invertible, regardless of whether it is left or right singular. However, in the context of singular value decomposition (SVD), the term "left singular vector" is used to describe a vector that, when multiplied by the singular values and the right singular vectors, reconstructs the original matrix.

In summary, while "vänstersingulära" is a term that can be encountered in the study of matrices and linear transformations, it is important to understand its context within the broader field of linear algebra. The term is not as commonly used as "singular" or "non-invertible," but it is a useful concept in the study of matrix decompositions and transformations.