Matrix

A rectangular grid of numbers; multiplying a vector by it applies a linear transformation.

A 2×2 matrix M has rows [a, b] and [c, d], and multiplying it by a vector x = [x₁, x₂] gives a new vector: M·x = [a·x₁ + b·x₂, c·x₁ + d·x₂] Each output entry is the dot product of one row with x.
From Matrices as transformations, step “A matrix moves vectors”

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Try matrix hands-on in the lesson Matrices as transformations, part of the The maths behind AI course.

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