Cramer's Rule Research Articles

Teaching Adjoint Networks to Juniors

This paper shows how the basic idea of the adjoint method can be taught to juniors using only sinusoidal steady-state analysis, Cramer's rule, a few matrix transpositions and the relation between node-admittance matrix and branch-admittance matrix.

The indefinite Z-transform technique and application to analysis of difference equations

The indefinite Z-transform technique is proposed. The method for solving linear difference equations using indefinite Z-transforms is compared with the methods employing the infinite one-sided Z-transforms and the finite Z-transforms. The distinct advantage of the method presented in this paper is that the desired solutions are obtained without employing standard inverse Z-transform techniques, such as the convolution theorem, or extensive Z-transform tables. All that is needed here for the derivations of the desired solutions is the application of Cramer's rule for the solution of simultaneous algebraic equations using the characteristic values. Therefore, this technique could be also readily used by those who have not studied the familiar Z-transform technique.

A Short Proof of Cramer's Rule

A Short Proof of Cramer's Rule

Using "Cross Products" to Derive Cramer's Rule

Using "Cross Products" to Derive Cramer's Rule

Using “Cross Products” to Derive Cramer's Rule

Using “Cross Products” to Derive Cramer's Rule

Existence and Uniqueness of Interpolating Rational Functions

(1962). Existence and Uniqueness of Interpolating Rational Functions. The American Mathematical Monthly: Vol. 69, No. 8, pp. 751-759.

A Vectorial Derivation of Cramer's Rule

A Vectorial Derivation of Cramer's Rule

On an Elementary Derivation of Cramer's Rule

On an Elementary Derivation of Cramer's Rule

Discussions: A Graphical Derivation of Cramer's Rule

Discussions: A Graphical Derivation of Cramer's Rule

The Theory of Determinants in the Historical Order of its Development

With Grunert it is necessary to take a long step backward. Although the memoirs of Bezout, Vandermonde, and Laplace were known to him, in addition to those of Hindenburg, Rothe, and Scherk, he advances only a short distance into the subject; his aim, indeed, is little more than the establishment of Cramer's rule for the solution of a set of simultaneous linear equations.His mode of presenting the subject, however, is fresh and interesting, the method of “undetermined multipliers” being taken to start with.