$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

# 5: Vector Spaces

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Some useful vector spaces:

R, the vector space of ordered n-tuples

P, the vector space of polynomials with real coefficients of degree less than or equal to n.

C the vector space of continuous functions - the interval can be specified as [a,b] or (-oo, oo)

Coo the vector space of continuous real-valued functions with infinitely many continuous derivatives - the interval can be specified as [a,b] or (-oo, oo)

Cn the vector space of continuous real-valued functions with n continuous derivatives - the interval can be specified as [a,b] or (-oo, oo)

F the vector space of all real-valued functions - the interval can be specified as [a,b] or (-oo, oo)

5: Vector Spaces is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.