Matrix ماتریس

The m rows are horizontal and the ncolumns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, a2,1represents the element at the second row and first column of a matrix A.

In mathematics, a matrix (plural: matrices) is a rectangular arrayof numberssymbols, or expressions, arranged in rows and columns.For example, the dimensions of the matrix below are 2 × 3 (read “two by three”), because there are two rows and three columns:

Addition, scalar multiplication and transposition

Operation Definition Example
Addition The sum A+B of two m-by-nmatrices A and B is calculated entrywise:

(A + B)i,j = Ai,j + Bi,j, where 1 ≤ i ≤ m and 1 ≤ j≤ n.
Scalar multiplication The product cA of a number c (also called a scalar in the parlance of abstract algebra) and a matrix A is computed by multiplying every entry of A by c:

(cA)i,j = c · Ai,j.

This operation is called scalar multiplication, but its result is not named “scalar product” to avoid confusion, since “scalar product” is sometimes used as a synonym for “inner product“.

Transposition The transpose of an m-by-nmatrix A is the n-by-m matrix AT (also denoted Atr or tA) formed by turning rows into columns and vice versa:

(AT)i,j = Aj,i.
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Familiar properties of numbers extend to these operations of matrices: for example, addition is commutative, that is, the matrix sum does not depend on the order of the summands: A + B = B + A.[12] The transpose is compatible with addition and scalar multiplication, as expressed by (cA)T = c(AT) and (A + B)T = AT + BT. Finally, (AT)T = A.

2 thoughts on “Matrix ماتریس

    1. چرا در حال بررسی زیر ساخت های این سیستم بودیم . گیف های تازه هم خواهیم داد .
      تشکر از همراهی تون

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