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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2006 • Question 1

Question

Math 6510 • Differentiable Manifolds Fall 2006 • Question 1

Show that the set \(M_1\) of real \(2\times 2\) matrices of rank 1 is a 3-dimensional submanifold of the space \(M(2,2)\cong \mathbb {R}^4\) of all real \(2\times 2\) matrices.

Raw LaTeX

Show that the set \(M_1\) of real \(2\times2\) matrices of rank 1 is a
3-dimensional submanifold of the space \(M(2,2)\cong\mathbb{R}^4\) of all real
\(2\times2\) matrices.

Topic Tags

Smooth Manifolds and Embedded Submanifolds