# Category:Matrix Algebra

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This category contains results about Matrix Algebra.

Definitions specific to this category can be found in Definitions/Matrix Algebra.

**Matrix algebra** is the subfield of algebra whose subjects of manipulation are matrices.

## Subcategories

This category has the following 24 subcategories, out of 24 total.

### D

### E

### G

### M

### N

### O

### R

### S

### T

### U

## Pages in category "Matrix Algebra"

The following 51 pages are in this category, out of 51 total.

### E

- Eigenvalue of Matrix Powers
- Elementary Matrix is Invertible
- Elementary Row Operation as Sequence of Other Two
- Elementary Row Operations by Matrix Multiplication
- Elementary Row Operations by Matrix Multiplication/Corollary
- Elementary Row Operations Commute with Matrix Multiplication
- Equivalence Relation on Square Matrices induced by Positive Integer Powers
- Equivalent Matrices have Equal Rank
- Equivalent Matrices may not be Similar

### I

### L

### M

- Matrix Equivalence is Equivalence Relation
- Matrix Form of Quaternion
- Matrix is Invertible iff Determinant has Multiplicative Inverse/Necessary Condition
- Matrix Multiplication Distributes over Matrix Addition
- Matrix Row Equivalent to Reduced Echelon Matrix
- Matrix Similarity is Equivalence Relation
- Matrix Space is Module

### R

### S

- Similar Matrices are Equivalent
- Special Linear Group is Subgroup of General Linear Group
- Square Matrices over Real Numbers under Multiplication form Monoid
- Square Matrix with Duplicate Columns has Zero Determinant
- Square Matrix with Duplicate Rows has Zero Determinant
- Square Matrix with Duplicate Rows has Zero Determinant/Corollary
- Square of Ones Matrix
- Substitution Rule for Matrices
- Substitution Rule for Matrices/Summation Convention