Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Matrix transformation
|
| gptkbp:alsoKnownAs |
Householder reflection
|
| gptkbp:application |
Eigenvalue algorithms
Reducing matrices to tridiagonal form Solving least squares problems |
| gptkbp:category |
Linear transformations
Matrix decompositions |
| gptkbp:definedIn |
H = I - 2vv^T
|
| gptkbp:dimensions |
n x n matrix
|
| gptkbp:heldBy |
Orthogonal transformation
Involutory matrix |
| https://www.w3.org/2000/01/rdf-schema#label |
Householder-Transformation
|
| gptkbp:location |
v is a unit vector
|
| gptkbp:mapType |
Vector to its mirror image
|
| gptkbp:namedAfter |
gptkb:Alston_Scott_Householder
|
| gptkbp:preserves |
Euclidean norm
|
| gptkbp:property |
Determinant is -1
Eigenvalues are 1 and -1 |
| gptkbp:usedIn |
gptkb:Linear_algebra
QR decomposition Numerical analysis |
| gptkbp:bfsParent |
gptkb:QR-Zerlegung
|
| gptkbp:bfsLayer |
7
|