linear algebra
Vectors and matrices
Linear algebra is the branch of mathematics dealing with vectors, matrices, and linear transformations—systems where outputs change proportionally with inputs.
It provides tools for solving systems of linear equations and understanding multidimensional space.
The subject is foundational to physics, computer graphics, machine learning, and statistics: The course covers linear algebra before differential equations.
Matrix-derived scalar quantity
- inverseOpposite in position
- transposeReverse order of elements
- rankPosition in hierarchy
- traceMinute remnant or pursue
identity · Gaussian elimination · pivot · cofactor · LU decomposition · unitary matrix · minor
Size or scale
- directionWay something faces
- dot productSum of component products
- cross productBinary vector operation
- basisUnderlying support or principle
normalization · projection · component · parallel · perpendicular · norm · eigenvector · coordinate
Transformation scaling constants
- eigenvectorsVectors scaled by matrices
- diagonalizationReducing to diagonal form
- LU decompositionMatrix split into triangular factors
- QR decompositionMatrix as orthogonal-triangular product
Subset forming smaller space
Turning on an axis
- scalingClimbing or resizing
- reflectionReturned light or thought
- shearLateral sliding force
- affineRelative by marriage
projective · isometry · dilation · contraction · perspective · mapping · invertible · image
Answer or liquid mixture
- unknownsUndetermined quantities
- coefficientsNumerical multipliers in expressions
- simultaneous equationsInterdependent mathematical relationships solved jointly
- homogeneousAlike in composition throughout
nonhomogeneous · substitution · elimination · consistent · inconsistent · underdetermined · overdetermined
determinant
Matrix-derived scalar quantity
trace · identity · Gaussian elimination · pivot · cofactor · LU decomposition · unitary matrix · minor
magnitude
Size or scale
- directionWay something faces
- dot productSum of component products
- cross productBinary vector operation
basis · normalization · projection · component · parallel · perpendicular · norm · eigenvector · coordinate · angle
eigenvalues
Transformation scaling constants
- eigenvectorsVectors scaled by matrices
- diagonalizationReducing to diagonal form
- LU decompositionMatrix split into triangular factors
subspace
Subset forming smaller space
rotation
Turning on an axis
- scalingClimbing or resizing
- reflectionReturned light or thought
- shearLateral sliding force
affine · projective · isometry · dilation · contraction · perspective · mapping · invertible · image · range
solution
Answer or liquid mixture
- unknownsUndetermined quantities
- coefficientsNumerical multipliers in expressions
- simultaneous equationsInterdependent mathematical relationships solved jointly
homogeneous · nonhomogeneous · substitution · elimination · consistent · inconsistent · underdetermined · overdetermined
wedge product
Antisymmetric tensor multiplication
- algebras
- mathaddition, subtraction, multiplication, division, fractions
- mathematicsarithmetic, calculus, geometry, number, addition
- computingcomputer, computers, software, hardware, code
- STEM subjectsmath, biology, chemistry, physics, calculus
- college coursesbiology, calculus, chemistry, physics, quantum physics
linear algebracalculus
Mathematical analysis system
chaos theory · analysis · differential equations · topology · differential calculus
algebra, linear, nonlinear, linearity, rectilinear, collinear, linearly