Applications of Inner Product Spaces
Author(s): M. Rajesh
Publication #: 2410042
Date of Publication: 26.10.2024
Country: India
Pages: 1-11
Published In: Volume 10 Issue 5 October-2024
Abstract
The aim of the present paper is to know the applications of Inner product spaces.
We can approximate a line or a polynomial for a set of points in the plane. The method of approximating a line or a polynomial for a set of points in the plane s the method of least squares. An inner product of two vectors in a vector space is a scalar which is the product of transpose of first vector and second vector. The cosine angle between two vectors can be find by using the inner product and the length of vectors. We defined orthogonal vectors, orthonormal vectors, orthogonal basis and orthonormal basis and Gram-Schmidt orthogonalization process.
By using the least squares method, we can find a line or polynomial for a given set of points in the plane. By using the method of least squares we can approximate exponential, logarithmic and trigonometric functions to a line or a polynomial.
Keywords: Inner product, Norm of a vector, angle between two vectors, orthogonal vectors, orthonormal vectors, Schwarz’s inequality, Triangle inequality, Pythagoras theorem, Gram-Schmidt orthogonalization process, the method of least squares.
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