Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:builtBy |
gptkb:Gram-Schmidt_process
|
| gptkbp:defines |
A basis whose vectors are mutually orthogonal and of unit length
|
| gptkbp:enables |
Diagonalization of symmetric matrices
Simple coordinate representation Simplifies inner product computation |
| gptkbp:example |
Standard basis in R^n
|
| gptkbp:field |
gptkb:Linear_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Orthonormal basis
|
| gptkbp:notation |
{e₁, e₂, ..., eₙ}
|
| gptkbp:property |
Any vector can be uniquely represented as a linear combination of basis vectors
Vectors are normalized Vectors are orthogonal |
| gptkbp:relatedTo |
gptkb:Vector
Basis (linear algebra) Orthonormal set |
| gptkbp:usedIn |
gptkb:Euclidean_space
gptkb:Hilbert_space gptkb:signal_processing gptkb:Quantum_mechanics Fourier analysis |
| gptkbp:bfsParent |
gptkb:Hilbert_Space
|
| gptkbp:bfsLayer |
6
|