Maths for ML / Notation

\mathbf{A}^{-1}

matrix inverse

Linear algebraIntermediate

Say it “A inverse”

The matrix that undoes A: A⁻¹A = I. Only exists for square, non-singular matrices.

Example

\mathbf{w} = (\mathbf{X}^{\top}\mathbf{X})^{-1}\mathbf{X}^{\top}\mathbf{y}

Closed-form linear regression.

In code

np.linalg.inv(A)  # prefer np.linalg.solve

torch.linalg.inv(A)

Where you’ll see it in ML

Closed-form solutions, Gaussian processes, whitening.

Don’t confuse it with

$\mathbf{A}^{\top}$ transpose Flip a matrix over its diagonal: rows become columns. Turns a column vector into a row vector.
$\mathbf{I}_n$ identity matrix Square matrix with 1s on the diagonal and 0s elsewhere. Multiplying by it changes nothing.
$\det(\mathbf{A}),\ |\mathbf{A}|$ determinant One number that says how much A scales area/volume. Zero means A squashes space flat and has no inverse.

Lessons that use it

Transpose, identity, inverse and determinant

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