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The Solution of Linear Algebraic Equations

Published online by Cambridge University Press:  03 November 2016

L. Brand
L. Brand*
Affiliation:
University of Houston, Texas, U.S.A.
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Extract

The rank of the coefficient matrix plays a dominant role in the theory of linear algebraic equations. It is not surprising, therefore, that a test for the rank of a matrix, that was a by-product of some work in dimensional analysis, proves to be an an admirable tool in this theory With its aid the consistency requirement assumes a simple and effective form, and the solution of both homogeneous and non-homogeneous systems is given explicitly in terms of submatrices.

Type
Research Article
Information
The Mathematical Gazette , Volume 46 , Issue 357 , October 1962 , pp. 203 - 207
Copyright
Copyright © Mathematical Association 1962

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References

page note 203 * L. Brand, The Pi Theorem in Dimensional Analysis, Archive for Rational Mechanics and Analysis, vol. 1, 1957, pp. 35-45. Presented in an invited address before the Texas section of the A.M.A., Waco, April, 1958.

page note 203 † Presented, with applications, in a paper “Test for the Rank of a Matrix” before the Texas section of the A.M.A., San Antonio, April 8, 1960.

page note 203 * See Bôcher, Introduction to Higher Algebra, Macmillan, New York, 1922, Chap. 4.