Define a vector space. Give an example.

Hey..! vector space is the set of objects known as vectors, we can add and multiply the vector by a number called scalars. It is also known as linear space.

Each element in vector space is a member of an object having a specific length known as a vector. Following are some examples of vector space.

Example:

  • Real Vector space is a vector space where scalers are real numbers.
  • Complex Vector Space: A vector space where scalers are complex numbers.
  • Trivial vector space: It is a vector space that contains only the zero vector, {0}.

Important things about Vector space

  • Vector space elements are known as N-tuples, n(length of each element).
  • Each element in vector space can be represented in matrix form.
  • Scalers are usually considered as Real Numbers.

Is zero a vector space?

Trivial vector{0}, is an example of vector space.

Vidyanju
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