## How to Determine if a Vector Set is Linearly Independent

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 [...]

## The Convolution Integral Explained

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 [...]

## Finding the Inverse of a Matrix

Posted by Luke on Mar 5, 2011 in Basic Electrical Engineering Concepts, Math

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 [...]

## Solving a Linear System Using the Inverse Matrix

Posted by Luke on Mar 3, 2011 in Basic Electrical Engineering Concepts, Linear Systems, Math

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 [...]

## Time Shifting and Scaling of Functions

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 [...]