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Wikipedia
scalar multiplication : In mathematics, scalar multiplication, also known as multiplication, is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra). Note that scalar multiplication is different from scalar product which is an inner product between two vectors. More specifically, if K is a field and V is a vector space over K, then scalar multiplication is a function from K × V to V. The result of applying this function to c in K and v in V is denoted c v. Scalar multiplication obeys the following rules (vector in boldface): Here + is addition either in the field or in the vector space, as appropriate; and 0 is the additive identity in either. Juxtaposition indicates either scalar multiplication or the multiplication operation in the field. Scalar multiplication may be viewed as an external binary operation or as an action of the field on the vector space. A geometric interpretation to scala.... More from Wikipedia
scalar multiplication : In abstract algebra, extension of scalars is a means of producing a module over a ring from a module over another ring , given a homomorphism between them. Intuitively, the new module admits multiplication by more scalars than the original.. More from Wikipedia
Scalar Multiple of a Vector
Multiplication of Vectors by Real Numbers, i.e., Scalar Multiple of a Vector - The multiplication of a vector by a real number assumes a lot of significance in such statements as - velocity of car B is double the velocity of car A l . When a vector is multipl..
Multiplication of Vectors by Real Numbers, i.e., Scalar Multiple of a Vector - The multiplication of a vector by a real number assumes a lot of significance in such statements as - velocity of car B is double the velocity of car A l . When a vector is multipl..Multiplication of Vectors by Real Numbers, i.e., Scalar Multiple of a Vector
The multiplication of a vector by a real number assumes a lot of significance in such statements as - velocity of car B is double the velocity of car A l..
More on Matrix Addition and Scalar Multiplication
www.mindbites.com Professor Burger shows you how to add and subtract vectors and use scalar multiplication to elongate or shrink vectors while maintaining their direction angle. The magnitude of a vector can be altered with scalar multiplication. A scalar is simply a number (positive or negative or a fraction) used to multiply a vector by, with the vector keeping its same direction and changing magnitude. Vectors can also be added and subtracted by simply adding or subtracting the components. ...