What is orthogonality and what makes a matrix orthogonal?
In this video, we build up orthogonality from the ground up, starting from the familiar idea of perpendicular vectors. You will see how the scalar product defines angles between vectors, what it means for vectors and matrices to be orthogonal, and why orthogonal matrices are particularly clean to work with.
Check out my full Linear Algebra playlist here: https://www.youtube.com/playlist?list=PLlenrM60CLlM1C6JDdtVBz1LOzIwTSNCm
📌 Timestamps:
0:00 Introduction
1:12 Scalar Product and L2-Norm
4:11 Orthogonal Vectors
5:49 Orthonormal Vectors
7:37 Orthogonal Matrices
12:39 Properties of Orthogonal Matrices
15:48 Toy Example
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