By Lawrence P. Huelsman
This high-level textual content explains the math at the back of easy circuit thought. It covers matrix algebra, which provides a normal technique of formulating the main points of a linear procedure. moreover, the writer provides the fundamental idea of n-dimensional areas and demonstrates its software to linear structures. Numerous problems look through the textual content. 1963 variation.
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Additional info for Circuits, matrices and linear vector spaces
In fact, the expansion is exactly that which would occur if the elements of the first and the second rows were identical. , the result of such an expansion, must be zero. For example, for the array an expansion in terms of the elements of the first row and the cofactors of the elements of the second row yields It is easily seen that this is exactly the expansion that would result from expanding the array along its second row. A similar proof applies to columns. Property 6 To any row of an array of elements can be added a multiple of any other row without changing the value of the determinant of the array.
1 We can establish an intuitive feeling for this case by assuming for the moment that only one of the Ui is nonzero, and that det A is also nonzero. If we divide the first equation of (6) by the second, we obtain This result is independent of both Ui and det A; therefore it should be valid for the case in which Ui and det A are zero. Thus, the choice of either of these variables determines the other. In considering both the above cases we conclude that a homogeneous set of equations has non-trivial solutions if and only if the determinant is equal to zero.
1961. A clear and readable introductory treatment. , O. Wing, and R. , New York, 1961. Notable for its conciseness. An excellent review text. Stewart, J. , New York, 1956. Especially good for its treatment and practical emphasis of pole-zero concepts and normalizations. Van Valkenburg, M. , 1955. One of the first texts with a modern treatment of its subject. Very well written. 1 The letter s is used in many texts for the complex frequency variable. The use of p is preferable, however, since s is also widely used to denote elastance (reciprocal capacitance).