ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Enclosed binary operation
Groupoid
Ringoid
Semiring
Ring
Left ring action
Module
Linear combination
Linear map
Multilinear map
Bilinear map
Sesquilinear map
Hermitian map
Hermitian form
Semi-inner product
Inner product
Inner product space
Gram-Schmidt projection
Euclidean complex Gram-Schmidt projection
Definition D5985
Euclidean real Gram-Schmidt projection
Formulation 3
Let $x, y \in \mathbb{R}^{N \times 1}$ each be a D5200: Real column matrix.
The Gram-Schmidt projection for $(x, y)$ is the D5200: Real column matrix \begin{equation} \frac{x^T y}{y^T y} y \end{equation}