Refers to the [vector space](Vector%20spaces.md), $M_n(\mathbb{R})$, of $n \times n$ matrices with elements on $\mathbb{R}$. Its dual space [map](Maps.md)s onto the field, $\mathbb{R}$. # Real inner product spaces [real inner product](Inner%20products.md#Real%20inner%20product) # Examples of real vector spaces * The real [$L^2(I)$ space.](L2(I)%20space.md) * The [[Euclidean space]] (ignoring extensions in $\mathbb{C}$). #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/VectorSpaces