Exercise 1.3.27

Question

Let $\mathrm{V}$ denote the vector space of all upper triangular $n 	imes n$ matrices (as defined on page 19), and let $\mathrm{W}_{1}$ denote the subspace of $\mathrm{V}$ consisting of all diagonal matrices. Define $\mathrm{W}_{2}=\left\{A \in \mathrm{V}: A_{i j}=0ight.$ whenever $\left.i \geq jight\}$. Show that $\mathrm{V}=\mathrm{W}_{1} \oplus \mathrm{W}_{2}$.

Jephian C.-H. Lin · Accepted Answer

This is similar to \href{./exercise_1-3-24}{Exercise 1.3.24}.

Exercise 1.3.27

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Exercise 1.3.27

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