(New page: A matrix can be thought of as an array of numbers. It is usually denoted by a capital letter (such as M), and each component (called an entry) can be denoted <math>M_{ij}</math> where ...) |
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1 & 2 & 3 \\ | 1 & 2 & 3 \\ | ||
4 & 5 & 6 \end{bmatrix}</math> | 4 & 5 & 6 \end{bmatrix}</math> | ||
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A matrix can be used to | A matrix can be used to | ||
* represent coefficients for a [[system of linear equations]] | * represent coefficients for a [[system of linear equations]] | ||
* represent a [[linear transformation]] | * represent a [[linear transformation]] | ||
* represent a [[basis]] of vectors | * represent a [[basis]] of vectors | ||
| − | * represent information where [[matrix multiplication]] has a meaning attached | + | * represent information where [[matrix multiplication]] has a meaning attached (Examples include a [[permutation matrix]] and an [[adjacency matrix]]) |
| − | (Examples include a [[permutation matrix]] and an [[adjacency matrix]]) | + | |
Revision as of 12:49, 18 January 2009
A matrix can be thought of as an array of numbers. It is usually denoted by a capital letter (such as M), and each component (called an entry) can be denoted $ M_{ij} $ where i is the row number (starting from 1) and j is the column number (starting from 1). A matrix can have any number of rows and columns, depending on the context. When referring to an arbitrary matrix of a given size i rows by j columns it can be denoted $ M_{ixj} $
For example, the following is a 2x3 matrix: $ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} $
A matrix can be used to
- represent coefficients for a system of linear equations
- represent a linear transformation
- represent a basis of vectors
- represent information where matrix multiplication has a meaning attached (Examples include a permutation matrix and an adjacency matrix)
