Matrices as transformations
A matrix is a machine that moves every point of space at once. Once you see that, matrix multiplication, determinants, inverses and rank each become one picture.
45 min
After this lesson you can
- Read the columns of a matrix as the places the basis vectors land
- Compute a matrix–vector product two ways, as a combination of columns and as a stack of dot products
- Explain why matrix multiplication is composition, and why the order matters
- Interpret the determinant as signed area scaling and connect it to invertibility
- Define column space, null space and rank, and check shapes before multiplying
In this lesson
- What makes a transformation “linear”
- A matrix is a record of where the basis vectors land
- Matrix times vector, two ways
- Matrix times matrix is doing one move, then another
- Shapes: the rule you’ll use every day
- The determinant: how much area changes
- Undoing a transformation: the inverse
- Rank, column space and null space
- In code
This lesson is part of Descent Pro
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