Summary of The determinant | Chapter 6, Essence of linear algebra

00:00:00 - 00:05:00

The determinant of a matrix is a useful tool for measuring how a linear transformation changes an area. In 3 dimensions, the determinant is also the volume of a parallelepiped that the cube turns into. The determinant is a natural way to describe orientation flipping, and it tells you how much a transformation scales things in 2 dimensions and 3 dimensions.

• 00:00:00 The determinant is a useful tool for measuring how a linear transformation changes an area. It can be negative if the transformation inverts the orientation of space.
• 00:05:00 The determinant is a natural way to describe orientation flipping, and it tells you how much a transformation scales things in 2 dimensions and 3 dimensions. In 3 dimensions, the determinant is also the volume of a parallelepiped that the cube turns into. If both b and c are non-0, then the b * c term tells you how much the parallelepiped is stretched or squished in the diagonal direction.