Category: Linear Algebra

As a last approach, we consider Cramer’s rule, which is a handy way to solve systems of two or three equations. The theory behind it requires more advanced concepts, such as matrices and their determinants, which are introduced below. We anticipate here a few concepts so that readers not interested in advanced multivariate statistics can… Continue reading Cramer’s rule

Gaussian elimination, with some improvements, is the basis of most numerical routines to solve systems of linear equations. Its rationale is that the following system is easy to solve: Such a system is said to be in upper triangular form, as nonzero coefficients form a triangle in the upper part of the layout. A system in… Continue reading Gaussian elimination

A basic (highschool) approach to solving a system of linear equations is substitution of variables. The idea is best illustrated by a simple example. Consider the following system: Rearranging the first equation, we may express the first variable as a function of the second one: and plug this expression into the second equation: Then we… Continue reading Substitution of variables

The theory, as well as the computational practice, of solving systems of linear equations is relevant in a huge list of real-life settings. In this section we just outline the basic solution methods, without paying due attention to bothering issues such as the existence and uniqueness of a solution, or numerical precision. A linear equation… Continue reading SOLVING SYSTEMS OF LINEAR EQUATIONS

Options are financial derivatives that have gained importance, as well as a bad reputation, over the years. In Section 1.3.1 we considered forward contracts, another type of derivative. With a forward contract, two parties agree on exchanging an asset or a commodity, called the underlying asset, at a prescribed time in the future, for a fixed price determined… Continue reading A MOTIVATING EXAMPLE: BINOMIAL OPTION PRICING