Maths 3.3Lesson outlineLesson 3 of 7 in Module 3
Identity, Inverse and Singular Matrices
Use the inverse as the transformation that undoes another, and know when it cannot exist.
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In this lesson12 parts
- 01Undoing a transformation
- 02The identity matrix
- 03The inverse
- 04Undoing two steps
- 05Singular matrices
- 06Nearly singular, and the condition number
- 07The determinant is not the test
- 08Checkpoint: inverses so far
- 09Temperature entered twice
- 10The check that sees it
- 11Inverses in NumPy
- 12Recap, challenge, and next: least squares
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- identity matrix
I, ones on the diagonal and zeros elsewhere; it leaves every vector unchanged |np.eye(2)- inverse
A⁻¹, the matrix that undoesA:A⁻¹A = AA⁻¹ = I|[[1, −1], [−1, 2]]- singular matrix
- a square matrix with no inverse; it flattens at least one direction, and its determinant is zero |
[[1, 2], [2, 4]] - rank
- the number of dimensions a matrix's output fills |
1for the singular example - condition number
- how much a matrix can magnify a small relative change; 1 is perfect, and large means nearly singular |
25,008for[[1, 2], [2, 4.001]]
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.