English Dictionary

invertible matrix

名詞

(linear algebra) Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix).

日本語の意味

線形代数において、ある n×n 正方行列が逆行列を持つ場合、その行列を指します。すなわち、存在する逆行列と掛け合わせることで、どちらの順序であっても n×n の単位行列が得られる行列です。

If the coefficient matrix is an invertible matrix, then the linear system has a unique solution.

係数行列が逆行列を持つ n×n の正方行列であれば、その線形方程式系は一意解を持つ。

意味（1）

(linear algebra) Any n×n square matrix for which there exists a corresponding inverse matrix (i.e., a second (or possibly the same) matrix such that when the two are multiplied by each other, in either order, the result is the n×n identity matrix).

It says that, if A is a singular matrix, then every neighborhood of A contains an invertible matrix. In other words, if A is singular, we can perturb A just a little and obtain an invertible matrix.

invertible matrices （ plural ）