“inverse matrix”的概念、定义、翻译、参考文献-科学参考

inverse matrix

Mathematics

An inverse of a square matrix A is a matrix X such that AX = I and XA = I. (A matrix that is not square cannot have an inverse, though it may have a left inverse or a right inverse.) A square matrix A may or may not have an inverse, but if it has then that inverse is unique and A is said to be invertible. A matrix is invertible if and only if it is not singular. Consequently, the term ‘non‐singular’ is sometimes used for ‘invertible’.

When det A ≠ 0, the matrix (1/detA) adjA is the inverse of A, where adjA is the adjugate of A. For example, the 2×2 matrix A below is invertible if ad − bc ≠ 0, and its inverse A⁻¹ is as shown:

$A = [\begin{matrix} a & b \\ c & d \end{matrix}], A^{- 1} = \frac{1}{a d - b c} [\begin{matrix} d & - b \\ - c & a \end{matrix}] .$

Statistics

See matrix.

Computer

For a given n×n matrix of numbers, A, if there is an n×n matrix B for which
$A B = B A = I$
where I denotes the identity matrix, then B is the inverse matrix of A and A is said to be invertible with B. If it exists, B is unique and is denoted by A⁻¹.

单词	inverse matrix
释义	inverse matrix Mathematics An inverse of a square matrix A is a matrix X such that AX = I and XA = I. (A matrix that is not square cannot have an inverse, though it may have a left inverse or a right inverse.) A square matrix A may or may not have an inverse, but if it has then that inverse is unique and A is said to be invertible. A matrix is invertible if and only if it is not singular. Consequently, the term ‘non‐singular’ is sometimes used for ‘invertible’. When det A ≠ 0, the matrix (1/detA) adjA is the inverse of A, where adjA is the adjugate of A. For example, the 2×2 matrix A below is invertible if ad − bc ≠ 0, and its inverse A⁻¹ is as shown: $A = [\begin{matrix} a & b \\ c & d \end{matrix}], A^{- 1} = \frac{1}{a d - b c} [\begin{matrix} d & - b \\ - c & a \end{matrix}] .$ Statistics See matrix. Computer For a given n×n matrix of numbers, A, if there is an n×n matrix B for which $A B = B A = I$ where I denotes the identity matrix, then B is the inverse matrix of A and A is said to be invertible with B. If it exists, B is unique and is denoted by A⁻¹.
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