Math Visualization List
Determinant
2x2 & 3x3 Determinants
Cramer's Rule
Permutations & Inversions
Permutation Definition & Expansion
Properties of Determinants: Row Operations
Minors & Cofactors
Two-Row Laplace Expansion
Vandermonde Determinant
Matrix Operations
Matrix Addition, Subtraction & Scalar Multiplication
Matrix Multiplication & Power
Transpose, Determinant & Adjoint
Inverse Matrix & Matrix Equations
Elementary Transformations, Echelon & Canonical Form
Probability & Statistics
Conditional Probability, Independence & Total Probability
Discrete Probability Distributions
PMF & CDF
2D Random Vectors
Conditional Probability Distributions
Bayes' Theorem
Numerical Characteristics of Random Variables
Higher Moments & Covariance Matrix
Law of Iterated Expectations
Independence, Mean Independence & Uncorrelated
Continuous Statistical Distributions
Vector Operations
Vector Addition, Subtraction & Scalar Multiplication
Linear Combination, Span & Basis
Matrices as Transformations
Composition of Transformations
3D Linear Transformations
Determinant
Inverse, Column Space & Rank
Cross-Dimensional Transformations
Vector Angle
Cross Product
Change of Basis
Eigenvectors & Eigenvalues
Function Vector Spaces
Geometric Interpretation of Cramer's Rule
Gravity Simulation
Composition of Transformations
Matrix multiplication C = AB means: Apply transformation B first, then apply transformation A.
Demo Steps:
Matrix A (Applied Second)
(Current: Rotate 90°)
Matrix B (Applied First)
Bî
Bĵ
(Current: Stretch + Shear)
Why "Row × Column"?
The first column of composed matrix C = AB is where basis vector î ends up.
1. î is first transformed by B to Column 1 of B.
2. This result is then transformed by A.
Column 1 of C = A × (Column 1 of B)
[ ?, ? ] =
A ×
[ 2, 0 ]
Similarly for Column 2 of C:
[ ?, ? ] =
A ×
[ 1, 1 ]