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Reference
https://en.wikipedia.org/wiki/Matrix_(mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.[1][2] For example, the dimension of the matrix below is 2 × 3 (read "two by three"), because there are two rows and three columns:
{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.}{\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.} Provided that they have the same dimensions (each matrix has the same number of rows and the same number of columns as the other), two matrices can be added or subtracted element by element (see conformable matrix). The rule for matrix multiplication, however, is that two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second (that is, the inner dimensions are the same, n for an (m×n)-matrix times an (n×p)-matrix, resulting in an (m×p)-matrix). Even when two matrices have dimensions allowing them to be multiplied in either order, the results need not be the same. That is, matrix multiplication is not, in general, commutative. Any matrix can be multiplied element-wise by a scalar from its associated field. Matrices are often denoted by capital roman letters such as {\displaystyle A}A, {\displaystyle B}B and {\displaystyle C}C.[3]
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Important
A matrix is a rectangular array of numbers (or other mathematical objects) for which operations such as addition and multiplication are defined.
[8] Most commonly, a matrix over a field F is a rectangular array of scalars, each of which is a member of F.[9][10] Most of this article focuses on real and complex matrices, that is, matrices whose elements are respectively real numbers or complex numbers. More general types of entries are discussed below. For instance, this is a real matrix:
{\displaystyle \mathbf {A} ={\begin{bmatrix}-1.3&0.6\\20.4&5.5\\9.7&-6.2\end{bmatrix}}.}{\displaystyle \mathbf {A} ={\begin{bmatrix}-1.3&0.6\\20.4&5.5\\9.7&-6.2\end{bmatrix}}.} The numbers, symbols, or expressions in the matrix are called its entries or its elements. The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively.
Size The size of a matrix is defined by the number of rows and columns that it contains. A matrix with m rows and n columns is called an m × n matrix, or m-by-n matrix, while m and n are called its dimensions. For example, the matrix A above is a 3 × 2 matrix.
Matrices with a single row are called row vectors, and those with a single column are called column vectors. A matrix with the same number of rows and columns is called a square matrix.[11] A matrix with an infinite number of rows or columns (or both) is called an infinite matrix. In some contexts, such as computer algebra programs, it is useful to consider a matrix with no rows or no columns, called an empty matrix.
https://en.wikipedia.org/wiki/Matrix_(mathematics)
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