Posted by Luke on Mar 24, 2011 in
Math
TweetPre-(r)amble The odds favor that by the time someone has reached this article, myself included, they have spent at least the briefest of moments (frustratedly?) questioning the practical applications for linear combination, linear independence and linear math. In a sentence, these concepts allow us to mathematically understand and represent multidimensional coordinate systems. If you’re looking [...]
Tags: coefficient, dependence, dependent, free, independence, independent, linear, matrix, pivot, variable
TweetIntroduction to the convolution Amongst the concepts that cause the most confusion to electrical engineering students, the Convolution Integral stands as a repeat offender. As such, the point of this article is to explain what a convolution integral is, why engineers need it, and the math behind it. In essence, the “convolution” of two functions [...]
Tags: convolutio integral, convolution, convolution integrals, convolution table, convolution tables, impulse response, Linear Systems
TweetMatrix manipulations and properties Finding the inverse of a matrix is much more complex than finding the inverse of a number. All real numbers have an inverse (i.e. ). However, not all matrices have an inverse. There are several characteristics that allow us to visibly determine whether a matrix has an inverse but we will [...]
Tags: identity matrix, inverse, inverse matrix property, matrix, matrix theory, rref
TweetDescribing the process of solving a linear system using the adjacent matrix is best done while performing an example. Suppose we have a system where is the coefficient matrix of our system, is the column vector containing our variables, and is the solution column vector. We are asked to solve for the column vector made [...]
Tags: coefficient matrix, inverse matrix, matrix, matrix division, matrix multiplication, matrix theory, solving linear systems, using inverse matrices
TweetWe’ll begin with a square function, f(t), that has a an amplitude of 1, a start time of 2 seconds and an end time of 4 seconds. Next, a time shift is demonstrated. Here our function is changed from f(t) to f(t-2). Notice that subtracting 2 from t in the function results in a positive [...]
Tags: amplitude, duration, function, graph, scale, shift, signal, time
