Phase 2 · Math, when you need it · Linear algebra
Matrices as transformations
A matrix stretches, rotates and projects space.
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Why it matters
So far a matrix has been a table of data. There's a second way to see one: as a machine that moves every point on a page. It can stretch the page, turn it, slant it or squash it. That's what each layer of a neural network does to its inputs. It bends the space until things that should be told apart (spam and not spam, one topic and another) sit in different places, easy to separate. Seeing matrices as motions makes deep learning feel like geometry instead of bookkeeping.
What you'll be able to do
- See a matrix as a function that moves every point of space
- Read a 2×2 matrix's columns as where the basis vectors land
- Recognize scaling, rotation, shear, reflection and projection matrices
- Use the determinant to tell how much a transformation stretches, flips or flattens space
Before this lesson
Next in this phase: Transpose, identity and inverse