Multiplication and Dot Product Operator

Operators > Algebra Operators > Multiplication and Dot Product Operator

Operator	Keyboard Shortcut
	*

Operands

x and y	Description
Two scalars	Returns the product of x and y.
Two vectors of the same length	Returns the dot product (inner product) of x and y: a scalar formed by multiplying element-wise the entries of the first vector with the complex conjugate of the entries of the second vector and summing the results.
An m x n and an n x p matrix	Returns an m x p matrix which is the matrix product of x and y.
An array and a scalar, in any combination	Returns an array formed by multiplying element-wise the entries of the array with the scalar.

Additional Information

• You can type expressions such as 5y without inserting the multiplication operator. The scaling operator is automatically inserted between the 5 and the y, and it acts as a multiplication operator.

• The scaling operator may not be visible unless you click on the region that contains it. It is recommended that you explicitly use the multiplication operators between expressions that you wish to multiply.

• The dot product (inner product) of two vectors has the following properties:

◦ x · y = |u| · |v| · cos(θ) where θ is the angle between the vectors.

◦ When x and y are orthogonal, their dot product is zero.

◦ The dot product of x with itself is the square of the length of x.

• To calculate the term-by-term product of two arrays of equal size, select the entire expression and insert the vectorize operator.