Learning Algebra 3

26th Nov, 2021

Three-dimensional linear transformations | Chapter 5

k̂ (k hat) is the unit vector for the Z direction.

A 3d vector transformation is the same as a 2D one, but with the extra dimension:

You also multiply 3d matrices the same way. From right to left.

The determinant | Chapter 6

The determinant of a linear transformation is the scaling factor by which it changes any area:

A negative determinant means space gets flipped over.

How to calculate it for 2D:

How to calculate it for 3D:

Inverse matrices, column space and null space | Chapter 7

For a matrix transformation A, the inverse of that is A^-1. And multiplying A by A^-1 (A inverse) is the equivalent of applying no transformation:

This is also called the identity transformation.

I didn't take a lot out of this chapter. I couldn't visualize how this would be useful for me, but I'm sure eventually I'll return here with a new found appreciation.