Linear algebra hub
Work with vectors, matrices, determinants, dot products, cross products, systems, and structured LaTeX.
Topic overview
Track operand type, dimensions, basis, and output type before performing a vector or matrix operation.
Recommended order
Identify scalar, vector, or matrix operands
Check dimensions and orientation
Apply the operation
Verify output type and reconstruction
Match the page to your intent
Popular searches
Avoid these errors
Interactive workflow
Step-by-step explanations
Linear algebra
Compare dot and cross products by output type, geometry, coordinate formulas, units, and common applications in mathematics and physics.
Read guideLinear algebra
Format determinant bars, matrices, minors, and named determinant expressions.
Read guideLinear algebra
Choose arrow, bold, component, and unit-vector notation for vectors in LaTeX.
Read guideComparisons
Understand how context distinguishes scalar multiplication, dot products, and decimal dots.
Read guideLaTeX
Build matrices with rows, columns, delimiters, alignment, and common environments.
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
Multiply matrices by checking dimensions, taking row-by-column dot products, and verifying the shape and selected entries.
Read guideComparisons
Know when to use ≈, =, ≡, and other relation symbols.
Read guideReviewed notation
\cdot\times\nabla\perp\angle\doteq\approx\because\between\bumpeqVariables 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 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 formulaAlgebra
a_n=a_1+(n-1)dFinds the nth term of a sequence with a constant difference.
Open formulaExplore nearby topics
Identify scalar, vector, or matrix operands
Read matrix and vector notation Generate matrix LaTeX Verify common vector operations
Multiplying incompatible dimensions