Difference between revisions of "Category:Linear Algebra"

2

• 2-Dimensional rotation matrix

A

• A linear map is injective if and only if its kernel is trivial
• A linear map is injective if and only if the image of every non-zero vector is a non-zero vector
• A linear map is injective if and only if the kernel contains only the zero vector
• A proper vector subspace of a topological vector space has no interior
• Addition of vector spaces
• Algebra
• Algebra (disambiguation)

B

• Basis
• Basis (linear algebra)
• Basis and coordinates
• Basis for the tensor product
• Bilinear form
• Bilinear map
• Bounded
• Bounded (linear map)
• Bounded linear map

C

• Canonical linear map
• Characteristic property of the tensor product
• Characteristic property of the tensor product/Statement
• Complex functionals
• Covector
• Covector applied to a tensor product

D

• Derivative (analysis)
• Notes:Dual basis
• Dual vector space

E

• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere
• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/1 implies 2
• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/2 implies 3
• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/3 implies 4

E cont.

• Equivalent conditions for a linear map between two normed spaces to be continuous everywhere/4 implies 1
• Euclidean norm
• Example comparing bilinear to linear maps
• External direct sum

F

• For a vector subspace of a topological vector space if there exists a non-empty open set contained in the subspace then the spaces are equal
• Formal linear combination
• Formal linear combination/Definition
• Free vector space generated by

G

• Geometrically independent set

H

• Homomorphism
• Homomorphism (vector space)

I

• Inner product
• Template:Inner product and Hilbert spaces navbox
• Isometry

K

• Kernel
• Kronecker delta

L

• Line
• Linear Algebra
• Linear Algebra (subject)
• Template:Linear algebra navbox
• Linear combination
• Linear functional
• Linear functionals
• Linear independence
• Linear isometry
• Linear map
• Linear maps
• Linear transform

M

• Matrix
• Multilinear map

M cont.

• Multilinear maps

N

• Natural linear map
• Norm
• Normed space

O

• Orthogonal complement
• Orthogonal vectors

P

• Projector
• Pullback norm

Q

• Quotient
• Quotient vector space

R

• Rotation matrix
• R^n is a topological vector space

S

• Set of all linear maps between spaces
• Space of all k-linear maps
• Span
• Span (linear algebra)
• Span, linear independence, linear dependence, basis and dimension
• Subspace

T

• Tensor product of vector spaces
• The closure of a linear subspace of a normed space is a linear subspace
• The dual space to the dual space of a vector space is canonically isomorphic to the vector space
• The space of all linear maps between spaces
• The vector space of all linear maps between two spaces
• Topological vector space
• Trivial

V

• Vector dot product
• Vector space
• Vector space of linear maps between spaces
• Vector spaces

W

• Wedge