# Accession Number:

## AD0712680

# Title:

## ON THE SOLUTION OF LINEAR ALGEBRAIC SYSTEMS BY MATRIX DECOMPOSITION.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## HAWAII UNIV HONOLULU

# Personal Author(s):

# Report Date:

## 1970-07-01

# Pagination or Media Count:

## 24.0

# Abstract:

A theorem is proved which states that the inverse matrix A sup-1sub n of any nonsingular matrix A sub n could be expressed as a unique sequence of U supisub n D supisub n L supisub n products where D supisub n is an n-th order diagonal matrix, U supisub n is a special n-th order upper triangular matrix, L supisub n is a special n-th order lower triangular matrix and i runs from 1 up to n. It is also shown that the inverse of each principal minor matrix A sub k with detA sub k not o is also generated in product form. Furthermore the non-zero column above the diagonal of each U supisub n is the solution of the system A subi-1Xsubi-1Csubi0 where C sub i a sub K,i, 1 or k or i-1. The associated algorithm is described together with considerations on storage arrangement, pivoting and operational counts. Finally an example is given in the Appendix. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics