Maths 3.1Lesson outlineLesson 1 of 7 in Module 3

Matrices, the Matrix–Vector Product and the Transpose

See a dataset as a matrix, and a linear model's predictions as one matrix–vector product.

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The words this lesson introduces, each in one line. The module’s glossary collects them all.

matrix: a rectangular table of numbers, treated as one object; rows are samples, columns are features | X = [[2, 1], [0, 3], [4, 2]]
shape: the number of rows, then the number of columns | (3, 2)
entry: one number in a matrix, xᵢⱼ | x₃₂ = 2
matrix–vector product: each row of the matrix dotted with the vector, one output per row | Xw = (5, −3, 10)
linear combination: vectors, each multiplied by a number, then added | 3·col₁ − 1·col₂
shape rule: the matrix's number of columns must equal the vector's length; the result has one entry per row | (3, 2) @ (2,) → (3,)
transpose: rows become columns; an n × d matrix becomes d × n | Xᵀ, (2, 3)
column mean: the average of one column, one number per feature | (2, 2)
centred matrix: each column minus its mean, so every column mean is zero | [[0, −1], [−2, 1], [2, 0]]