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Portfolio Construction and Analytics by Dessislava A. Pachamanova, Frank J. Fabozzi

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Appendix

Basic Linear Algebra Concepts

This appendix provides a very basic introduction to linear algebra concepts. Some of these concepts are intentionally presented here in a somewhat simplified (not as general as it could be) form. Our goal is not to teach all intricacies of this very important field in mathematics, but to enable readers to understand the linear algebra notation and applications described in this book.

A.1 Systems of Equations

Consider a very simple equation:

equation

In this equation, x is a variable, and a and b are input data. To find the value of the variable x, we would simply write

equation

Equivalently, we could have written

equation

Consider now a simple system of two linear equations:

equation

The variables in this system are bapp01-math-0005 and bapp01-math-0006, and the input data consist of the coefficients 3, 8, 10, and the constants to the right of the equal sign, 46 and . The way we would normally solve this system ...

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