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## 5.2 Matrix Arithmetic Operators

Stan supports the basic matrix operations using infix, prefix and postfix operations. This section lists the operations supported by Stan along with their argument and result types.

### 5.2.1 Negation Prefix Operators

vector operator-(vector x)
The negation of the vector x.

row_vector operator-(row_vector x)
The negation of the row vector x.

matrix operator-(matrix x)
The negation of the matrix x.

### 5.2.2 Infix Matrix Operators

vector operator+(vector x, vector y)
The sum of the vectors x and y.

row_vector operator+(row_vector x, row_vector y)
The sum of the row vectors x and y.

matrix operator+(matrix x, matrix y)
The sum of the matrices x and y

vector operator-(vector x, vector y)
The difference between the vectors x and y.

row_vector operator-(row_vector x, row_vector y)
The difference between the row vectors x and y

matrix operator-(matrix x, matrix y)
The difference between the matrices x and y

vector operator*(real x, vector y)
The product of the scalar x and vector y

row_vector operator*(real x, row_vector y)
The product of the scalar x and the row vector y

matrix operator*(real x, matrix y)
The product of the scalar x and the matrix y

vector operator*(vector x, real y)
The product of the scalar y and vector x

matrix operator*(vector x, row_vector y)
The product of the vector x and row vector y

row_vector operator*(row_vector x, real y)
The product of the scalar y and row vector x

real operator*(row_vector x, vector y)
The product of the row vector x and vector y

row_vector operator*(row_vector x, matrix y)
The product of the row vector x and matrix y

matrix operator*(matrix x, real y)
The product of the scalar y and matrix x

vector operator*(matrix x, vector y)
The product of the matrix x and vector y

matrix operator*(matrix x, matrix y)
The product of the matrices x and y

vector operator+(vector x, real y)
The result of adding y to every entry in the vector x

vector operator+(real x, vector y)
The result of adding x to every entry in the vector y

row_vector operator+(row_vector x, real y)
The result of adding y to every entry in the row vector x

row_vector operator+(real x, row_vector y)
The result of adding x to every entry in the row vector y

matrix operator+(matrix x, real y)
The result of adding y to every entry in the matrix x

matrix operator+(real x, matrix y)
The result of adding x to every entry in the matrix y

vector operator-(vector x, real y)
The result of subtracting y from every entry in the vector x

vector operator-(real x, vector y)
The result of adding x to every entry in the negation of the vector y

row_vector operator-(row_vector x, real y)
The result of subtracting y from every entry in the row vector x

row_vector operator-(real x, row_vector y)
The result of adding x to every entry in the negation of the row vector y

matrix operator-(matrix x, real y)
The result of subtracting y from every entry in the matrix x

matrix operator-(real x, matrix y)
The result of adding x to every entry in negation of the matrix y

vector operator/(vector x, real y)
The result of dividing each entry in the vector x by y

row_vector operator/(row_vector x, real y)
The result of dividing each entry in the row vector x by y

matrix operator/(matrix x, real y)
The result of dividing each entry in the matrix x by y

### 5.2.4 Elementwise Arithmetic Operations

vector operator.*(vector x, vector y)
The elementwise product of y and x

row_vector operator.*(row_vector x, row_vector y)
The elementwise product of y and x

matrix operator.*(matrix x, matrix y)
The elementwise product of y and x

vector operator./(vector x, vector y)
The elementwise quotient of y and x

vector operator./(vector x, real y)
The elementwise quotient of y and x

vector operator./(real x, vector y)
The elementwise quotient of y and x

row_vector operator./(row_vector x, row_vector y)
The elementwise quotient of y and x

row_vector operator./(row_vector x, real y)
The elementwise quotient of y and x

row_vector operator./(real x, row_vector y)
The elementwise quotient of y and x

matrix operator./(matrix x, matrix y)
The elementwise quotient of y and x

matrix operator./(matrix x, real y)
The elementwise quotient of y and x

matrix operator./(real x, matrix y)
The elementwise quotient of y and x