## 6.2 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.

### 6.2.1 Negation prefix operators

vector operator-(vector x)
The negation of the vector x.
Available since 2.0

row_vector operator-(row_vector x)
The negation of the row vector x.
Available since 2.0

matrix operator-(matrix x)
The negation of the matrix x.
Available since 2.0

T operator-(T x)
Vectorized version of operator-. If T x is a (possibly nested) array of matrix types, -x is the same shape array where each individual value is negated.
Available since 2.31

### 6.2.2 Infix matrix operators

vector operator+(vector x, vector y)
The sum of the vectors x and y.
Available since 2.0

row_vector operator+(row_vector x, row_vector y)
The sum of the row vectors x and y.
Available since 2.0

matrix operator+(matrix x, matrix y)
The sum of the matrices x and y
Available since 2.0

vector operator-(vector x, vector y)
The difference between the vectors x and y.
Available since 2.0

row_vector operator-(row_vector x, row_vector y)
The difference between the row vectors x and y
Available since 2.0

matrix operator-(matrix x, matrix y)
The difference between the matrices x and y
Available since 2.0

vector operator*(real x, vector y)
The product of the scalar x and vector y
Available since 2.0

row_vector operator*(real x, row_vector y)
The product of the scalar x and the row vector y
Available since 2.0

matrix operator*(real x, matrix y)
The product of the scalar x and the matrix y
Available since 2.0

vector operator*(vector x, real y)
The product of the scalar y and vector x
Available since 2.0

matrix operator*(vector x, row_vector y)
The product of the vector x and row vector y
Available since 2.0

row_vector operator*(row_vector x, real y)
The product of the scalar y and row vector x
Available since 2.0

real operator*(row_vector x, vector y)
The product of the row vector x and vector y
Available since 2.0

row_vector operator*(row_vector x, matrix y)
The product of the row vector x and matrix y
Available since 2.0

matrix operator*(matrix x, real y)
The product of the scalar y and matrix x
Available since 2.0

vector operator*(matrix x, vector y)
The product of the matrix x and vector y
Available since 2.0

matrix operator*(matrix x, matrix y)
The product of the matrices x and y
Available since 2.0

vector operator+(vector x, real y)
The result of adding y to every entry in the vector x
Available since 2.0

vector operator+(real x, vector y)
The result of adding x to every entry in the vector y
Available since 2.0

row_vector operator+(row_vector x, real y)
The result of adding y to every entry in the row vector x
Available since 2.0

row_vector operator+(real x, row_vector y)
The result of adding x to every entry in the row vector y
Available since 2.0

matrix operator+(matrix x, real y)
The result of adding y to every entry in the matrix x
Available since 2.0

matrix operator+(real x, matrix y)
The result of adding x to every entry in the matrix y
Available since 2.0

vector operator-(vector x, real y)
The result of subtracting y from every entry in the vector x
Available since 2.0

vector operator-(real x, vector y)
The result of adding x to every entry in the negation of the vector y
Available since 2.0

row_vector operator-(row_vector x, real y)
The result of subtracting y from every entry in the row vector x
Available since 2.0

row_vector operator-(real x, row_vector y)
The result of adding x to every entry in the negation of the row vector y
Available since 2.0

matrix operator-(matrix x, real y)
The result of subtracting y from every entry in the matrix x
Available since 2.0

matrix operator-(real x, matrix y)
The result of adding x to every entry in negation of the matrix y
Available since 2.0

vector operator/(vector x, real y)
The result of dividing each entry in the vector x by y
Available since 2.0

row_vector operator/(row_vector x, real y)
The result of dividing each entry in the row vector x by y
Available since 2.0

matrix operator/(matrix x, real y)
The result of dividing each entry in the matrix x by y
Available since 2.0