Scalar multiplication of a vector by a factor of 3 stretches the vector out.The scalar multiplications −a and 2a of a vector a
In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra[1][2][3] (or more generally, a module in abstract algebra[4][5]). In common geometrical contexts, scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction. Scalar multiplication is the multiplication of a vector by a scalar (where the product is a vector), and is to be distinguished from inner product of two vectors (where the product is a scalar).
^Lay, David C. (2006). Linear Algebra and Its Applications (3rd ed.). Addison–Wesley. ISBN 0-321-28713-4.
^Strang, Gilbert (2006). Linear Algebra and Its Applications (4th ed.). Brooks Cole. ISBN 0-03-010567-6.
^Axler, Sheldon (2002). Linear Algebra Done Right (2nd ed.). Springer. ISBN 0-387-98258-2.
^Dummit, David S.; Foote, Richard M. (2004). Abstract Algebra (3rd ed.). John Wiley & Sons. ISBN 0-471-43334-9.
^Lang, Serge (2002). Algebra. Graduate Texts in Mathematics. Springer. ISBN 0-387-95385-X.
and 23 Related for: Scalar multiplication information
In mathematics, scalarmultiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract...
generally, elements of any field. The operations of vector addition and scalarmultiplication must satisfy certain requirements, called vector axioms. Real vector...
Elliptic curve scalarmultiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic...
called scalars (from scale) to distinguish them from vectors. The operation of multiplying a vector by a scalar is called scalarmultiplication. The resulting...
\mathbf {u} +\mathbf {v} } Scalarmultiplication is represented in the same manners as algebraic multiplication. A scalar beside a vector (either or both...
product Matrix multiplication Metric tensor Multiplication of vectors Outer product The term scalar product means literally "product with a scalar as a result"...
consisting of a set together with operations of multiplication and addition and scalarmultiplication by elements of a field and satisfying the axioms...
scaling matrix, since matrix multiplication with it results in changing scale (size) and possibly also shape; only a scalar matrix results in uniform change...
scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalarmultiplication must satisfy...
vectors under the usual matrix multiplication operator: in one order they yield the dot product, which is just a scalar and as such a rank zero tensor...
{a} \mathbf {b} ^{\mathsf {T}}} Scalarmultiplication Matrix calculus, for the interaction of matrix multiplication with operations from calculus Nykamp...
an algebraic structure with an addition, a multiplication, and a scalarmultiplication (the multiplication by the image of the ring homomorphism of an...
vector spaces that preserves the operations of vector addition and scalarmultiplication. The same names and the same definition are also used for the more...
example, scalarmultiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar. Such...
"formal" scalarmultiplication—to give a vector field called the gradient; second, it can act on vector fields by a "formal" dot product—to give a scalar field...
used to determine the work done by a constant force. Scalarmultiplication Matrix multiplication Vector addition Vector algebra relations This article...
This set forms a supermodule over R under supermatrix addition and scalarmultiplication. In particular, if R is a superalgebra over a field K then Mr|s×p|q(R)...
{\displaystyle V,} but whose scalarmultiplication involves conjugation of the scalars. In other words, the scalarmultiplication of V ¯ {\displaystyle {\overline...
use × {\displaystyle \times } to denote elliptic curve point multiplication by a scalar. For Alice to sign a message m {\displaystyle m} , she follows...
\mathbf {b} )+(\mathbf {a} \times \mathbf {c} ),} and compatible with scalarmultiplication so that ( r a ) × b = a × ( r b ) = r ( a × b ) . {\displaystyle...
called a field, and an operation called scalarmultiplication between elements of the field (called scalars), and elements of the vector space (called...
property that the vector space operations (vector addition and scalarmultiplication) are also continuous functions. Such a topology is called a vector...
Global Information
