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}