Dashboard
Featured nodes
Roots
Public root
Templates
Test template
iCorps template
Guanyu's Latex template
Ivar's latex template
Family Tree template
Latex template
Router template
Trees
Public trees
Related nodes
Parents
1
Orthogonality
Siblings
24
Sort by title
Sort by date
Definition of angle between vectors
Definition of orthogonal vectors
Definition of parallel vectors
Two vectors are orthogonal if and only if the Pythagorean Theorem holds.
Definition of a vector being orthogonal to a subspace
Definition of orthogonal complement of a subspace
The orthogonal complement of a subspace is a subspace.
The direct sum of a subspace and its orthogonal complement is the whole space.
A vector is in the orthogonal complement of a subspace if and only if it is orthogonal to every vector in a basis of the subspace.
The null space of a matrix is the orthogonal complement of the column space.
Definition of orthogonal set of vectors
Definition of orthonormal set of vectors
An orthogonal set of nonzero vectors is linearly independent.
Definition of orthogonal basis of a (sub)space
Definition of orthonormal basis of a (sub)space
A matrix A with real entries has orthonormal columns if and only if A inverse equals A transpose.
A matrix with real entries and orthonormal columns preserves norms.
A matrix with real entries and orthonormal columns preserves dot products.
Formula for the coordinates of a vector with respect to an orthogonal/orthonormal basis.
A vector can be written uniquely as a sum of a vector in a subspace and a vector orthogonal to the subspace.
Description of the Gram-Schmidt process
The Gram-Schmidt process converts a linearly independent set into an orthogonal set.
Definition of Gram-Schmidt process
Definition of orthogonal subspaces
Knowen
β
Go to node
Help
Welcome to Knowen!
Edit test node (no login required)
Create new test node (no login required)
Not logged in
Sign in
Sign up
3
Privacy
Edit node
Two vectors are orthogonal if and only if the Pythagorean Theorem holds.
Created almost 9 years ago
A
−
A
+
Put content here.
Parents
Orthogonality