MQL5 ReferenceLanguage BasicsOperatorsMatrix product operator

Matrix product operator @

The @ MQL5 operator implements matrix multiplication according to the rules of linear algebra. It allows multiplying matrices and vectors, as well as performing scalar multiplication of vectors.

Supported element types:

float
double
complex<float>
complex<double>

Important: The element types in the left and right operands must match.

Examples of use

1. Matrix multiplication (matrix × matrix)

matrix A(2, 3);
matrix B(3, 2);
matrix C = A @ B; // Result: Matrix C of size [2,2]

2. Matrix multiplication (matrix × vector)

matrix M(2, 3);
vector V(3);
vector R = M @ V; // Result: Vector R of 2 elements

3. Matrix multiplication (vector x matrix)

matrix M(2, 3);
vector V(1, 2);
vector R = V @ M; // Result: Vector R of 3 elements

4. Scalar multiplication (vector × vector)

vector V1(1, 3), V2(1, 3);
double r = V1 @ V2; // Result: Scalar

Note

The dimensions must comply with the rules of multiplication: the number of columns in the first operand = the number of rows in the second.

In case of a dimension error, an exception will be triggered at runtime.

Vectors on the left are considered horizontal (1×n).

Vectors on the right are considered vertical (n×1).

The priority of the @ operation corresponds to the priority of multiplication, i.e. for an entry of D=C+A@B, first matrix multiplication T=A@B is performed, followed by the element-wise addition D=C+T.