2.1 Matrices Intro - #02 Matrices: What are they? Motivation and Essence (Special)

What is a matrix? What are matrices used for? Why are they important? What are their applications? What do they represent?

This lecture introduces matrices as representing linear transformations of vectors. We define linear transformations, learn how to visualize them and how to describe them analytically, and then learn how they can be equivalent to a matrix multiplication. We give the general recipe and tricks to remember matrix-vector multiplication.

King's College London - Physics Programme -
Year 1 Maths Video Lecture

CONTENTS:
- Why are matrices important? [00:05]
- What are transformations? [02:14]
- What are linear transformations? Definition [04:09]
- Scalar multiplication vs Matrix multiplication [06:48]
- Visualization of 2D linear transformations [09:56]
- Lines are transformed into lines [11:52]
- Examples of 2D linear transformations [13:46]
- Analytical description of linear transformations and visual interpretation [14:15]
- Relation between linear transformation and matrix [20:13]
- General matrix-vector multiplication [22:47 & 24:49]
- Visual trick to remember matrix multiplication [27:00]

Francisco (Paco) Rodríguez Fortuño
Senior Lecturer King's College London