Linear Algebra in LaTeX: Vectors, Matrices, and Transformations

Linear algebra has some of the richest notation in LaTeX. This guide covers vectors, matrices, determinants, eigenvalues, and more.

Vectors

Use \\vec{v} for arrow notation, \\mathbf{v} for bold. Column vectors: \\begin{pmatrix} v_1 \\\\ v_2 \\\\ v_3 \\end{pmatrix}.

Matrix Operations

Multiplication: (AB)_{ij} = \\sum_k A_{ik} B_{kj}. Transpose: A^{\\mathsf{T}} or A^{\\top}.

Eigenvalues

A\\vec{v} = \\lambda\\vec{v}. Characteristic polynomial: \\det(A - \\lambda I) = 0.

Special Matrices

Identity: I_n. Zero: \\mathbf{0}. Diagonal: \\operatorname{diag}(d_1, \\ldots, d_n).