Linear algebra
How to Calculate a 2×2 Determinant
Calculate the determinant of a 2×2 matrix, interpret zero versus nonzero results, and verify signs and row operations.
Read guidePrimary topic hub
Linear Algebra and Matrix Guides
Work with vectors, matrices, determinants, eigenvalues, decompositions, projections, least squares, coordinate changes, and systems of equations.
Focused guides
4 indexed guides
These pages each serve a distinct task and pass the source, specificity, and duplication gates.
Linear algebra
How to Multiply Matrices
Multiply matrices by checking dimensions, taking row-by-column dot products, and verifying the shape and selected entries.
Read guideLinear algebra
How to Write Determinants in LaTeX
Format determinant bars, matrices, minors, and named determinant expressions.
Read guideLinear algebra
How to Write Vectors in LaTeX
Choose arrow, bold, component, and unit-vector notation for vectors in LaTeX.
Read guideBrowse 18 supporting references
These pages answer narrower notation questions and link back to this hub; they are intentionally noindex to reduce cannibalization.
Linear Algebra
Basis and Coordinate Changes
Separate vectors from coordinate columns and define change-of-basis matrices.
Read guideLinear algebra
Bold, Arrow, and Matrix Notation for Vectors
Choose a consistent visual convention for vectors, matrices, scalars, and coordinate components.
Read guideLinear algebra
Dot Product vs Cross Product
Compare dot and cross products by output type, geometry, coordinate formulas, units, and common applications in mathematics and physics.
Read guideLinear Algebra
Eigenvalue and Eigenvector Notation
Define right and left eigenvectors, multiplicities, normalization, and spectra.
Read guideEigenvalues and Eigenvectors
Eigenvalues and Eigenvectors: Common Errors and Verification
Common Errors and Verification for eigenvalues and eigenvectors: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notati
Read guideEigenvalues and Eigenvectors
Eigenvalues and Eigenvectors: LaTeX Formatting Guide
LaTeX Formatting Guide for eigenvalues and eigenvectors: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideEigenvalues and Eigenvectors
Eigenvalues and Eigenvectors: Notation Reference
Notation Reference for eigenvalues and eigenvectors: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideLeast Squares
Least Squares: Common Errors and Verification
Common Errors and Verification for least squares: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideLeast Squares
Least Squares: LaTeX Formatting Guide
LaTeX Formatting Guide for least squares: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideLeast Squares
Least Squares: Notation Reference
Notation Reference for least squares: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideMatrix Algebra
Matrix Algebra: Common Errors and Verification
Common Errors and Verification for matrix algebra: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideMatrix Algebra
Matrix Algebra: LaTeX Formatting Guide
LaTeX Formatting Guide for matrix algebra: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideMatrix Algebra
Matrix Algebra: Notation Reference
Notation Reference for matrix algebra: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideLinear Algebra
Matrix Decomposition Notation
Compare LU, QR, eigenvalue, singular-value, and Cholesky decompositions.
Read guideLinear algebra
Matrix Operations: Add, Multiply, Transpose, and Check Dimensions
Understand the dimension rules behind matrix addition, multiplication, and transposition before using an online calculator.
Read guideLinear Algebra
Orthogonality and Projection
Write inner products, orthogonal complements, projection matrices, and residuals.
Read guideLinear Algebra
Positive-Definite Matrix Notation
Compare positive definite, semidefinite, symmetric, and Hermitian conditions.
Read guideLinear Algebra
Singular Value Decomposition Notation
Track matrix shapes, singular vectors, singular values, rank, and truncation.
Read guide