# 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