Category:Linear Algebra
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This category contains results about Linear Algebra.
Definitions specific to this category can be found in Definitions/Linear Algebra.
Linear algebra is the branch of algebra which studies vector spaces and linear transformations between them.
Subcategories
This category has the following 70 subcategories, out of 70 total.
A
B
C
D
- Dimension of Proper Subspace (1 P)
- Direct Sums (1 P)
- Discriminants (empty)
E
- Examples of Linear Equation (2 P)
F
- Floquet's Theorem (3 P)
G
- Generators of Modules (4 P)
- Grassmann's Identity (3 P)
H
J
- Jordan Canonical Form (1 P)
L
- Linear Dependence (4 P)
- Linear Forms (empty)
- Linear Independence (12 P)
M
- Matrix Spaces (1 P)
N
O
- Orthonormal Bases of Vector Spaces (empty)
P
- Polarization Identity (3 P)
Q
R
- Representation Theory (11 P)
S
- Scalar Multiplication (9 P)
- Similarity Mappings (6 P)
- Standard Ordered Bases (4 P)
T
U
V
Z
Pages in category "Linear Algebra"
The following 89 pages are in this category, out of 89 total.
C
- Cauchy-Bunyakovsky-Schwarz Inequality
- Cayley-Hamilton Theorem/Matrices
- Change of Basis Matrix under Linear Transformation
- Characterization of Left Null Space
- Complex Numbers form Vector Space over Reals
- Complex Numbers form Vector Space over Themselves
- Composition of Linear Real Functions
- Condition for Composition of Linear Real Functions to be Commutative
- Condition for Planes to be Parallel
- Conditions for Homogeneity
- Conditions for Homogeneity/Plane
- Conditions for Homogeneity/Straight Line
- Conjugate Transpose is Involution
- Content of Cayley-Menger Determinant
- Cramer's Rule
D
E
- Eigenvalues of Hermitian Operator have Orthogonal Eigenspaces
- Equation of Plane
- Equation of Straight Line in Plane
- Equivalence of Definitions of Change of Basis Matrix
- Equivalent Statements for Vector Subspace Dimension One Less
- Existence of Minimal Polynomial for Square Matrix over Field
- Existence of Ordered Dual Basis
- Existence of Scalar for Vector Subspace Dimension One Less
- Expression of Vector as Linear Combination from Basis is Unique
- Expression of Vector as Linear Combination from Basis is Unique/General Result
G
H
I
L
N
P
R
- Rank and Nullity of Transpose
- Rank Plus Nullity Theorem
- Rational Numbers form Vector Space
- Real Linear Subspace Contains Zero Vector
- Real Numbers form Vector Space
- Real Symmetric Matrix is Hermitian
- Results concerning Generators and Bases of Vector Spaces
- Right Product with Degenerate Linear Transformation is Degenerate
- Row Equivalent Matrix for Homogeneous System has same Solutions
- Row Equivalent Matrix for Homogeneous System has same Solutions/Corollary