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What is Vector Spaces and Matrices about?

In the preceding chapter, vectors were looked at from three different perspectives. In this chapter, the notion of vectors has been formalized by introducing vector space, a “structured” space where vectors reside. The relationships between (a) two sets—V, a nonempty set of vectors and F, a scalar field and (b) two algebraic operations—addition and scalar multiplication have been axiomatically defined. Vectors in a given set are linearly independent of each other or one can be expressed as a linear combination of the others. The linear combinations are given formal structures by means of basis vectors and coordinate systems. To geometrically conceptualize vector spaces, vector norms and vector distances have been defined, first in terms of dot products and, subsequently, in the language of general inner products. Special emphasis has been given to the notion of orthogonality that has a pivotal role in the analysis and application of vector spaces.

Author

Subrata Pal

Publisher

Elsevier Science & Technology

Published

2023

Language

EN

ISBN

9780323903974

Subjects

Science, Mathematics, Biology