VECTOR SPACE
Vector spaces play a role in many branches of mathematics and its
applications .In fact,in various practical problems we have a set X
whose elements may be vectors in three-dimensional space, or spectrum
of numbers,or function,and these elements can be added and multiplied
by constants in a natural way,the result being again an element of X.
Such concrete situations suggest the concept of a vector space as defined below.
The definition will involve a general field K.but in functional analysis,K will be R or C. The elements of K are called scalars;hence in our case they will be real or complex numbers.
Vector spaces play a role in many branches of mathematics and its
applications .In fact,in various practical problems we have a set X
whose elements may be vectors in three-dimensional space, or spectrum
of numbers,or function,and these elements can be added and multiplied
by constants in a natural way,the result being again an element of X.
Such concrete situations suggest the concept of a vector space as defined below.
The definition will involve a general field K.but in functional analysis,K will be R or C. The elements of K are called scalars;hence in our case they will be real or complex numbers.
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