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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2017 • Question 2

Question

Math 6510 • Differentiable Manifolds Spring 2017 • Question 2

Let \(A:\mathbb {R}^n\to \mathbb {R}^n\) be linear and let \(\phi \in \Lambda ^n(\mathbb {R}^n)\). Prove \(A^*\phi =\det (A)\phi \).

Raw LaTeX

Let \(A:\R^n\to\R^n\) be linear and let \(\phi\in\Lambda^n(\R^n)\). Prove
\(A^*\phi=\det(A)\phi\).

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