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What is Linear Independence: An Explanation by Example

In this post we define linear independence and walk through an example to develop an intuitive understanding of the concept. What is Linear Independence? When a set of several vectors is linearly independent, it is not possible to represent one vector as a linear combination of the remaining vectors in the set. Two orthogonal vectors

Dot Product and Orthogonal Vectors

In this post, we learn how to calculate the dot product between two vectors. Furthermore, we look at orthogonal vectors and see how they relate to the dot product. What is the Inner Product? The inner product of two vectors is the sum of the element-wise products of two vectors. The result of the

Unit Vector: Background and Definition

In this short post, we will learn how to calculate the magnitude of a vector and how to obtain the unit vector. The magnitude of a Vector A vector has a direction and a magnitude (or length). The following vector has a direction of 1 on the x-axis and 3 on the y-axis.  But

Basic Vector Operations

In this post build a basic understanding of vectors and learn how to perform vector addition, vector subtraction, and vector scaling in a multidimensional space. We also take a brief look at how vectors can be used to construct matrices. What is a vector? A vector is an array of numbers that are arranged