Author: user

This tutorial explains how mean can be viewed as an orthogonal projection onto a subspace defined by the span of an all 1’s vector (i.e., basis vector). Suppose that \( \vec{y} \in \mathbb{R}^n \) and \( L \subset \mathbb{R}^n\) is...

This tutorial explains what an orthogonal projection is in linear algebra. Further, it provides proof that the difference between a vector and a subspace is orthogonal to that subspace. Let’s define two vectors, \(\vec{X} \) and \(\vec{Y} \), and we...

Two Orthogonal Vectors Definition: Two vectors are orthogonal if they are perpendicular to each other. That is, the dot product of the two vectors is zero. The following is an example of two orthonormal vectors. \( \vec{V_1} =\left[\begin{array}{ccc}1\\0\\-1\end{array}\right]\), \( \vec{V_2}...