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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.
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However, in the special case of a conservative vector field, the value of the integral is independent of the path taken, which can be thought of as a large-scale cancellation of all elements that do not have a component along the straight line between the two points. To visualize this, imagine two people climbing a cliff; one decides to scale ...
Normally each element of a random vector is a real number. Random vectors are often used as the underlying implementation of various types of aggregate random variables , e.g. a random matrix , random tree , random sequence , stochastic process , etc.
The concept of productive matrix was developed by the economist Wassily Leontief (Nobel Prize in Economics in 1973) in order to model and analyze the relations between the different sectors of an economy. [1]
Another method of deriving vector and tensor derivative identities is to replace all occurrences of a vector in an algebraic identity by the del operator, provided that no variable occurs both inside and outside the scope of an operator or both inside the scope of one operator in a term and outside the scope of another operator in the same term ...
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