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Practical Scientific Computing by V Zalizniak, A Muhammad

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8

Solving Systems of Linear Equations

8.1 Linear Algebra Background

To begin with, we will consider some basic definitions from linear algebra needed for understanding of matrix computations. We will restrict our consideration to the case when matrices and vectors are real. Vectors, then, are objects of the N-dimensional Euclidean space RN. A list of the operations defined in RN follows.

• Addition:

image

• Multiplication by scalar:

image

In addition, there is correspondence between any pair of vectors x, y ∈ RN and a real scalar (x, y) called the dot ...

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