Editing Index notation (section)

===Two-dimensional arrays===
[[File:Matrix.svg|thumb|247px|right|Elements of matrix '''A''' are described with two subscripts or indices.]]
{{main|matrix (mathematics)}}
{{see also|Dyadics}}

More than one index is used to describe arrays of numbers, in two or more dimensions, such as the elements of a matrix, (see also image to right);

:<math>\mathbf{A} = \begin{pmatrix}
  a_{11} & a_{12} & \cdots & a_{1n} \\
  a_{21} & a_{22} & \cdots & a_{2n} \\
  \vdots & \vdots & \ddots & \vdots \\
  a_{m1} & a_{m2} & \cdots & a_{mn} \\
\end{pmatrix}</math>

The entry of a matrix '''A''' is written using two indices, say ''i'' and ''j'', with or without commas to separate the indices: ''a<sub>ij</sub>'' or ''a<sub>i,j</sub>'', where the first subscript is the row number and the second is the column number. [[Multiplication|Juxtaposition]] is also used as notation for multiplication; this may be a source of confusion. For example, if

:<math>\mathbf{A} = \begin{pmatrix}
  9 & 8 & 6 \\
  1 & 2 & 7 \\
  4 & 9 & 2 \\
  6 & 0 & 5 
\end{pmatrix}</math>

then some entries are

:<math>a_{11} = 9,\, a_{12} = 8,\, a_{21} = 1,\, \cdots,\, a_{23} = 7,\, \cdots </math>.

For indices larger than 9, the comma-based notation may be preferable (e.g., ''a''<sub>3,12</sub> instead of ''a''<sub>312</sub>).

[[Matrix equation]]s are written similarly to vector equations, such as

:<math> \mathbf{A} + \mathbf{B} = \mathbf{C} </math>

in terms of the elements of the matrices (aka components)

:<math> A_{ij} + B_{ij} = C_{ij} </math>

for all values of ''i'' and ''j''. Again this expression represents a set of equations, one for each index. If the matrices each have ''m'' rows and ''n'' columns, meaning {{nowrap|''i'' {{=}} 1, 2, …, ''m''}} and {{nowrap|''j'' {{=}} 1, 2, …, ''n''}}, then there are ''mn'' equations.