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Multiplication of (,,) by a scalar results in the multiplication of (,,) by the same scalar, and , and cannot be all unless , and are all zero since is nonsingular. So ( X , Y , Z ) {\displaystyle (X,Y,Z)} are a new system of homogeneous coordinates for the same point of the projective plane.
A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.
[1] [3] In North America, the term résumé (also spelled resume) is used, referring to a short career summary. [4] [5] The term curriculum vitae and its abbreviation, CV, are also used especially in academia to refer to extensive or even complete summaries of a person's career, qualifications, and education, including publications and other ...
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]).
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