A Rapid Review Of Theorems Based On Inner Product Spaces & Modified Theorem Based On Inner Product Spaces

In Mathematics, inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or scalar
product of Cartesian coordinates. Inner product spaces of infinite dimension are widely used in functional analysis. Inner product
spaces over the field of complex numbers are sometimes referred to as unitary spaces. An inner product is a generalization of the dot
product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. In this paper work
we will discuss about the inner product, its basic concepts necessary for theorem’s proof and various theorems based on inner product
spaces on real fields. Further, we modified the theorem of inner product spaces based on the symmetric and positive definite matrix
associated fields real.