elementary matrix

English

elementary matrix (plural elementary matrices)

(linear algebra) A square matrix which is obtained from the identity matrix by a single elementary row (or column) operation.
When an elementary matrix multiplies a square matrix from the left, it applies to that matrix an elementary row operation homologous to the one that created its own self. (Likewise, when an elementary matrix multiplies a square matrix from the right, it applies to that matrix an elementary column operation homologous to the one that created its own self.)
If a series of elementary matrices applied to a given square matrix row-reduce it to the identity matrix, then the same series of elementary matrices applied to the identity matrix yield the inverse of the given matrix.

单词	elementary matrix
释义	elementary matrix English Noun elementary matrix (plural elementary matrices) (linear algebra) A square matrix which is obtained from the identity matrix by a single elementary row (or column) operation. When an elementary matrix multiplies a square matrix from the left, it applies to that matrix an elementary row operation homologous to the one that created its own self. (Likewise, when an elementary matrix multiplies a square matrix from the right, it applies to that matrix an elementary column operation homologous to the one that created its own self.) If a series of elementary matrices applied to a given square matrix row-reduce it to the identity matrix, then the same series of elementary matrices applied to the identity matrix yield the inverse of the given matrix.
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