Matrix (mathematics)

For the square matrix section, see square matrix.

Definitions and notations

The horizontal lines in a matrix are called rows and the vertical lines are called columns. A matrix with m rows and n columns is called an m-by-n matrix (or m×n matrix) and m and n are called its dimensions.

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The entry of a matrix A that lies in the i -th row and the j-th column is called the i,j entry or (i,j)-th entry of A. This is written as Ai,j or A.

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We often write A:=(a_{i,j})_{m imes n} to define an m × n matrix A with each entry in the matrix A called aij for all 1 ? i ? m and 1 ? j ? n.

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Example

The matrix

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:egin{bmatrix}

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1 & 2 & 3 \

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1 & 2 & 7 \

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4&9&2 \

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6&0&5end{bmatrix}

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is a 4×3 matrix. The element A or a2,3 is 7.

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