16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 7.3.14
The Rational and Jordan Forms
Mathematics — Linear Algebra · jordan-form-skew-symmetric
Problem
What's wrong with the following proof? If A is a complex n×n matrix such that At=−A, then A is 0. (Proof: Let J be the Jordan form of A. Since At=−A, Jt=−J. But J is triangular so that Jt=−J implies that every entry of J is zero. Since J=0 and A is similar to J, we see that A=0.) (Give an example of a non-zero A such that At=−A.)