Dot

Dot (Operator)

Format

vectorA dot vectorB

returns float_expression or integer_expression depending on the type of the elements.

Description

Returns the dot product of two vectors — the two arrays multiplied element by element and added up. It is zero exactly when the two vectors are at right angles to each other.

Both vectors must hold the same number of elements, but they need not be the same shape: a row, a column, or whatever Mat Trn hands back all count as vectors, because the elements are read in the order they are stored.

If every element of both vectors is a whole number the answer is a whole number, and a fraction anywhere makes the answer a fraction.

dot binds more tightly than a comparison and less tightly than cross, so a dot b cross c is a dot (b cross c) and a dot b = 0 is (a dot b) = 0.

Example

print {1,2,3} dot {4,5,6}
print {3,4} dot {3,4}

# the cosine of the angle between two vectors
a = {1,0}
b = {0,1}
print (a dot b) / (norm(a) * norm(b))

will print

32
25
0

Errors

Error	Cause
136	An operand is not an array.
137	The two vectors have different numbers of elements.
139	An element of the vector has never been given a value.

See Also

Arrays, Cross, Mat, Norm, Unit, Vector Operators

History

2.2	New To Version