QR decomposition
Orthogonal-triangular matrix split
QR decomposition is a method of factoring a matrix into two components: Q, an orthogonal matrix, and R, an upper triangular matrix.
The technique is fundamental in numerical linear algebra for solving systems of equations, computing eigenvalues, and performing least-squares regression.
The algorithm uses QR decomposition to find the best-fit line.
A family name
- Gram-SchmidtVector orthogonalization algorithm
- factorizationDecomposing into multiplicative parts
- algorithmFinite problem-solving procedure
- numericalRelating to figures
MATLAB · iteration · stability · pivoting · floating-point · complexity · parallelization · sparse
Three-cornered in form
- unitaryForming a single entity
- rectangularFour right angles
- squareRhombus with right angles
- reducedMade less in amount
economy · rank · determinant · invertible · transpose
Error-minimizing statistical method
- eigenvaluesTransformation scaling constants
- regressionReturn to former state
- overdeterminedHaving excess determining factors
- curve fittingApproximating data mathematically
signal processing · optimization · residual · conditioning · ill-conditioned
Perpendicular and unit-length
- projectionSomething that extends outward
- perpendicularAt right angles
- basisUnderlying support or principle
- subspaceSubset forming smaller space
normalization · span · rotation · reflection · angle · coordinate system
Householder
A family name
- Gram-SchmidtVector orthogonalization algorithm
- factorizationDecomposing into multiplicative parts
- algorithmFinite problem-solving procedure
numerical · MATLAB · iteration · stability · pivoting · floating-point · complexity · parallelization · sparse · dense
triangular
Three-cornered in form
- unitaryForming a single entity
- rectangularFour right angles
- squareRhombus with right angles
reduced · economy · rank · determinant · invertible · transpose
least squares
Error-minimizing statistical method
- eigenvaluesTransformation scaling constants
- regressionReturn to former state
- overdeterminedHaving excess determining factors
curve fitting · signal processing · optimization · residual · conditioning · ill-conditioned
orthonormal
Perpendicular and unit-length
- projectionSomething that extends outward
- perpendicularAt right angles
- basisUnderlying support or principle
subspace · normalization · span · rotation · reflection · angle · coordinate system
- linear algebramatrix, linear equation, vectors, linear function, matrices
- Decompositionseigendecomposition, diagonalization, prime factorization, factoring, PCA
- dimensionality reductionPCA, eigenvalues, eigenvector, loading, component
- numerical methodsbisection, interpolation, Gaussian elimination, least squares, convergence
- matricestranspose, determinants, rows, cells, Hermitian matrices
- eigenvalueseigenvalue, eigenvector, eigenvalues, eigenvectors, eigendecomposition