Skip to main content

linear algebraic equations

linear algebraic equations (simultaneous equations) A problem in numerical linear algebra that requires the solution of n equations in the unknowns x1, x2,…, xn of the form Ax = b

where A is a square n×n matrix. The solution obtained by computing the inverse matrix and forming A–1b is less accurate and requires more arithmetical operations than elimination methods. In Gaussian elimination multiples of successive equations are added to all succeeding ones to eliminate the unknowns x1, x2,…, xn–1 in turn. Properly used, with row interchanges to avoid large multiples, this leads to a solution that satisfies exactly a system close to the one given, relative to the machine precision. The accuracy of the solution, which can be cheaply estimated, depends on the condition number of the problem.

Many other methods are used to deal with matrices of special form. Very large systems where the matrix A has predominantly zero entries occur in the solution of partial differential equations. Elimination methods tend to fill in the zeros causing storage problems and iterative methods are often preferred for such problems.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"linear algebraic equations." A Dictionary of Computing. . 25 Mar. 2019 <>.

"linear algebraic equations." A Dictionary of Computing. . (March 25, 2019).

"linear algebraic equations." A Dictionary of Computing. . Retrieved March 25, 2019 from

Learn more about citation styles

Citation styles gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, cannot guarantee each citation it generates. Therefore, it’s best to use citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

The Chicago Manual of Style

American Psychological Association

  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.