I have trouble with understanding following from my text book in Measures and Integral theory.
Let T be an orthogonal $n\times n$ matrix. If $\lambda^{n}$ is the Lebesgue measure then we have: $\lambda^{n} = T(\lambda^{n})$
And my question is:
How to interpret the $T(\lambda^{n})$-part?
How is it possible to multiply a $n\times n$ matrix with a real number ($\lambda^{n}$ is a measure and therefore it is a value between 0 and $\infty$)?