Category:Linear Algebra

A

• [+] Algebras‎ (1)

D

• [×] Determinants‎ (0)

M

• [+] Matrix Algebra‎ (1)
• [+] Module Theory‎ (6)

N

• [×] Normed Spaces‎ (0)

R

• [×] Representation Theory‎ (0)

T

• [×] Tensor Theory‎ (0)

V

• [+] Vector Algebra‎ (2)

V cont.

• [+] Vector Analysis‎ (1)
• [+] Vector Spaces‎ (2)
• [×] Vector Subspaces‎ (0)

B

• Bases of Finitely Generated Vector Space
• Basis for Finite Submodule of Function Space
• Basis for Finitely Generated Vector Space
• Basis of Vector Space is Linearly Independent and a Generator
• Basis of Vector Space of Polynomial Functions

C

• Cardinality of Generator No Less than Dimension
• Cardinality of Linearly Independent Set No Greater than Dimension
• Cauchy-Schwarz Inequality
• Change of Basis is Invertible
• Complex Vector Space
• Condition for Planes being Parallel
• Condition for Straight Lines being Parallel
• Conditions for Homogeneity

D

• Determinant of Linear Transformation Well Defined
• Differentiation on Polynomials is Linear Operator
• Dimension of Proper Subspace Less Than its Superspace
• Dimension of Sum and Intersection of Vector Spaces
• Division Ring is Vector Space over Prime Subfield

E

• Empty Set is Linearly Independent
• Equation of a Plane
• Equation of a Straight Line
• Equivalent Matrices have Equal Rank

F

• Floquet's Theorem

G

• Generated Submodule is Linear Combinations
• Generator of Vector Space Contains Basis

H

• Hermitian Matrices have Real Eigenvalues
• Hermitian Operators have Orthogonal Eigenvectors
• Hermitian Operators have Real Eigenvalues
• Hermitian Operators have Real Eigenvalues and Orthogonal Eigenvectors
• Homomorphic Image of Vector Space

I

• Integration on Polynomials is Linear Operator
• Invertible Matrix Corresponds with Change of Basis

L

• Linear Operator on the Plane
• Linear Transformation of Vector Space Equivalent Statements
• Linear Transformation of Vector Space Monomorphism
• Linear Transformations Isomorphic to Matrix Space
• Linearly Dependent Sequence of Vector Space
• Linearly Independent Subset also Independent in Generated Subspace
• Linearly Independent Subset of Basis of Vector Space
• Linearly Independent Subset of Finitely Generated Vector Space
• Lines are Subspaces of Plane

M

• Matrix Corresponding to Change of Basis under Linear Transformation

P

• Planes are Subspaces of Space
• Product of Vector Spaces
• Projection of Straight Line on Another in Plane

R

• Rank and Nullity of Transpose
• Rank is Dimension of Subspace
• Rank Plus Nullity Theorem
• Rational Numbers form Vector Space
• Real Numbers form Vector Space

R cont.

• Real Vector Space
• Reflection
• Results Concerning Annihilator of Vector Subspace
• Results concerning Generators and Bases of Vector Spaces

S

• Sequence containing Identity is Linearly Dependent
• Similarity
• Simultaneous Equation With Two Unknowns
• Singleton is Linearly Independent
• Solution to Simultaneous Linear Equations
• Standard Ordered Basis
• Stretching and Contraction
• Subset of Linearly Independent Set
• Subspaces of Dimension 2 Real Vector Space
• Superset of Linearly Dependent Set

U

• Unique Representation by Ordered Basis

V

• Vector Space of All Mappings
• Vector Space on Cartesian Product
• Vector Space over Division Subring
• Vector Space over Subring
• Vector Subspace Dimension One Less
• Vector Subspace Test

Z

• Zero Vector is Linearly Dependent
• Zero Vector Space Product iff Factor is Zero