Matrix

In Linear Algebra a $m \times n$ matrix $A$ is a rectangular array with $m$ rows and $n$ columns:

$A = \begin{bmatrix} a_{11} & a_{12} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a_{2n}\\ ... & ... & ... & ... \\ a_{m1} & a_{m2} & ... & a_{mn} \end{bmatrix}$

$\{a_{ij}\}$ (or $(A)_{ij}$) are components of the matrix $A$

if $m = n$, then $A$ is called rectangular

$(a_{11}, a_{22}, ..., a_{nn})$ are diagonal elements


Operations


Types

Matrices can be:


Decompositions


Matrices as Vectors

We can see matrices as vectors, and they also can form Vector Spaces


Sources

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