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Exercise 3

Avg difficulty 3.0

Show that this operation is an inner product on the real vector space M2 ⁣× ⁣2\mathcal{M}_{2\!\times\!2}.

⟨(abcd),(efgh)⟩=ae+bf+cg+dh\langle\begin{pmatrix}a&b\\ c&d\end{pmatrix},\begin{pmatrix}e&f\\ g&h\end{pmatrix}\rangle=ae+bf+cg+dh

Hefferon, Linear Algebra, Similarity, Inner Product, Exercise 3

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.