Maths That Models Change
Matrices & Transformations
14 min · 2 worked examplesStudent plan
A compact way to handle many equations at once, and the mathematics behind every robot arm and 3D rotation.
After this lesson you can
- Multiply two small matrices without losing track
- Apply a rotation to a point
- See why robot arm kinematics is matrix work
A grid of numbers with rules
A matrix is a rectangular array of numbers, and its size is quoted rows by columns. Its value is that it packages a whole system of linear equations into one object.
Addition is elementwise and unremarkable. Multiplication is the interesting one: to multiply, you take each row of the first matrix against each column of the second, multiplying pairs and summing. That means the first matrix must have as many columns as the second has rows, and it means matrix multiplication is not commutative. AB and BA are generally different, and often only one of them is even defined.
That non-commutativity is not a quirk. It is exactly why rotating an object about x then y gives a different result from y then x, as you can confirm with any solid object in your hand.
In the full lesson
- A grid of numbers with rules
- Solving systems
- Rotation and robot arms
This lesson comes with the Student plan. The first module of Maths for Engineers is free.