Matrix workflow hub
Create matrices in LaTeX, understand matrix notation, and verify determinants, row reduction, linear systems, and related calculations.
Topic overview
Matrix notation depends on dimensions, delimiters, indexing, and the operation being performed. This hub combines matrix authoring guides with calculators and formula references for common linear-algebra tasks.
Recommended order
Confirm the matrix dimensions and notation convention.
Choose an editor, generator, or calculator that matches the operation.
Check dimensions, assumptions, and numerical output independently.
Match the page to your intent
Popular searches
Avoid these errors
Interactive workflow
Step-by-step explanations
Linear algebra
Format determinant bars, matrices, minors, and named determinant expressions.
Read guideLaTeX
Build matrices with rows, columns, delimiters, alignment, and common environments.
Read guideLinear algebra
Understand the dimension rules behind matrix addition, multiplication, and transposition before using an online calculator.
Read guideMatrix Algebra
Notation Reference for matrix algebra: write, format, verify, and publish clear definitions, assumptions, examples, accessible markup, and portable notation.
Read guideLinear algebra
Calculate the determinant of a 2×2 matrix, interpret zero versus nonzero results, and verify signs and row operations.
Read guideLinear algebra
Choose arrow, bold, component, and unit-vector notation for vectors in LaTeX.
Read guideLinear algebra
Compare dot and cross products by output type, geometry, coordinate formulas, units, and common applications in mathematics and physics.
Read guideLinear algebra
Multiply matrices by checking dimensions, taking row-by-column dot products, and verifying the shape and selected entries.
Read guideReviewed notation
\cdot\times\cdots\otimes\vdots\nabla\perp\angle\doteqVariables and assumptions
Linear Algebra
\det\begin{pmatrix}a&b\\c&d\end{pmatrix}=ad-bcCalculates the determinant of a two-by-two matrix.
Open formulaLinear Algebra
\mathbf a\times\mathbf b=\begin{bmatrix}a_2b_3-a_3b_2\\a_3b_1-a_1b_3\\a_1b_2-a_2b_1\end{bmatrix}Calculates the three-dimensional vector cross product.
Open formulaLinear Algebra
\mathbf{a}\cdot\mathbf{b}=\sum_{i=1}^{n}a_ib_i=\|\mathbf{a}\|\|\mathbf{b}\|\cos\thetaCombines two vectors into a scalar and relates their components to the angle between them.
Open formulaLinear Algebra
A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}Finds the inverse of a nonsingular 2×2 matrix.
Open formulaGeometry
A=\pi r^2Calculates the area enclosed by a circle of radius r.
Open formulaGeometry
A=\frac{1}{2}bhCalculates triangle area from a base and its perpendicular height.
Open formulaExplore nearby topics
Confirm the matrix dimensions and notation convention.
Create matrices in LaTeX. Use browser-based matrix tools. Review common linear-algebra notation and formulas.
Multiplying matrices with incompatible dimensions.