elementary matrix
Hello, you have come here looking for the meaning of the word elementary matrix. In DICTIOUS you will not only get to know all the dictionary meanings for the word elementary matrix, but we will also tell you about its etymology, its characteristics and you will know how to say elementary matrix in singular and plural. Everything you need to know about the word elementary matrix you have here. The definition of the word elementary matrix will help you to be more precise and correct when speaking or writing your texts. Knowing the definition ofelementary matrix, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.
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.