INTRODUCTORY CONCEPTS AND OPERATIONS

Here denotes the coefficient of the th unknown xj in the ith equation, and the numbers aij and 6, (hence xj) all are real. Often the number m of equations is equal to the number n of unknowns, but exceptions are common in optimization and modeling and will be noted in Chapters 6 and 7. 

Array notations are convenient for such problems. Let the bold letters 

Methods for solving Eq. (A.1-1) can then be described in terms of operations on the arrays A and b. Before doing so. we pause to summarize a few essentials of linear algebra fuller treatments are given in Stewart (1973) and in Noble and Daniel (1988). 

Matrices can be added if their corresponding dimensions are equal. The addition is done element by element  

The difference A - B is formed analogously. It follows that two matrices are equal if their corresponding elements are equal their difference is then a zero matrix 0, with every element equal to zero. 

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