The rules for arithmetic operations between row vectors, are in fact the same as those for the arithmetic of lists, given in part in section Arithmetic for Lists, here we reiterate and complete that definition, in the language of vectors.
+ vec2 O
returns the sum of the two vectors vec1 and vec2, which must have the
same length and be defined over a common field. The sum is a new vector
where each entry is the sum of the corresponding entries of the vectors. As
an exception it is also possible to add an integer vector to a vector over
the finite field F, in which case the integers are interpreted as
scalar * One(F).
+ vec O
+ scalar O
returns a new vector where each entry is the sum of the scalar and the
corresponding entry of the vector. The elements of vec must lie in a
common field with scalar. As an exception it is also possible to add an
integer scalar to a vector over the finite field F, in which case the
integer is interpreted as scalar * One(F).
gap> [ 1, 2, 3 ] + [ 1/2, 1/3, 1/4 ]; [ 3/2, 7/3, 13/4 ] gap> [ 1/2, 3/2, 1/2 ] + 1/2; [ 1, 2, 1 ]
- vec2 O
- vec O
- scalar O
The difference operator - returns the componentwise difference of its
two operands and is defined subject to the same restrictions as +.
gap> [ 1, 2, 3 ] - [ 1/2, 1/3, 1/4 ]; [ 1/2, 5/3, 11/4 ] gap> [ 1/2, 3/2, 1/2 ] - 1/2; [ 0, 1, 0 ]
* vec2 O
returns the standard scalar product of vec1 and vec2, which must
both have the same length and take their entries from the same
field. As remarked above, the system only provides a general method
for the case where the vectors lie in IsRingElementList. The
product is the sum of the products of the corresponding entries of the
vectors. As an exception it is also possible to multiply an integer
vector to a finite field vector, in which case the integers are
interpreted as scalar * One(GF).
* vec O
* scalar O
returns the product of scalar and vector.
The elements of vec must lie in a common field with scalar.
The product is a new
vector where each entry is the product of the scalar and the
corresponding entry of the vector. As an exception it is also possible
to multiply an integer scalar to a finite field vector, in which case the
integer is interpreted as scalar * One(GF).
gap> [ 1, 2, 3 ] * [ 1/2, 1/3, 1/4 ]; 23/12 gap> [ 1/2, 3/2, 1/2 ] * 2; [ 1, 3, 1 ]
For the mutability of results of arithmetic operations, see Mutability and Copyability.
Further operations with vectors as operands are defined by the matrix operations (see Operators for Matrices).
NormedRowVector( v ) A
returns a scalar multiple w = c * v of the row vector v
with the property that the first nonzero entry of w is an identity
element in the sense of IsOne.
gap> NormedRowVector([5,2,3]); [ 1, 2/5, 3/5 ]
GAP 4 manual