Exercise 7.3

Question

Let $A$ be an $m 	imes m$ matrix, and let $a_j$ be its $j$th column. Give an algebraic proof of Hadamard's inequality:
$$|\det A| \leq \prod_{j=1}^{m} \|a_j\|_2.$$
Also give a geometric interpretation of this result, making use of the fact that the determinant equals the volume of a parallelepiped.

Desh Raj · Accepted Answer

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Exercise 7.3

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Exercise 7.3

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