Infinite Dimensional Vector Space

khyratmaths

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Dear Members
Kindly guide me about Infinite Dimensional Vector Space? I am requested to give easy examples Infinite Dimensional Vector Space with proof.
Waiting for good response.
 
Dear Members
Kindly guide me about Infinite Dimensional Vector Space? I am requested to give easy examples Infinite Dimensional Vector Space with proof.
Waiting for good response.
I don't see how it is possible to give a "good response" without knowing what you already know about this. Do you know what a "Vector Space" is? Do you know how the dimension of a vector space is defined?

Can you prove that the set of all quadratic polynomials, \(\displaystyle ax^2+ bx+ c\), with the usual addition of polynomials and multiplication by numbers, is a vector space? What is its dimension?

Same questions for the set of all sixth degree polynomials, \(\displaystyle ax^6+ bx^5+ cx^4+ dx^3+ ex^2+ fx+g\).

What about the set of all polynomials? What about the set of all continuous functions?
 
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