mathodman Posted June 17, 2019 Share Posted June 17, 2019 Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix. Link to comment Share on other sites More sharing options...
hypervalent_iodine Posted June 17, 2019 Share Posted June 17, 2019 ! Moderator Note We do not do other people's homework for them. Please show some attempt at an answer and explain here you are stuck. Link to comment Share on other sites More sharing options...
mathodman Posted June 18, 2019 Author Share Posted June 18, 2019 22 hours ago, hypervalent_iodine said: ! Moderator Note We do not do other people's homework for them. Please show some attempt at an answer and explain here you are stuck. Its not a homework, lol. Just an interesting problem, that i don't quite understand. I think that the only option is that A matrix is zero matrix or maybe i have forgotten some theorem or criteria Link to comment Share on other sites More sharing options...
MotleyNoumenon Posted July 8, 2019 Share Posted July 8, 2019 Well, as stated the first part has only one solution, the zero matrix; on the other hand the zero matrix is skew-symmetric.. The first part could be modified but why bother, its gonna be a rotation of \( \pi/2 \) radians in some direction, i.e. the solution space could be visualized as a circle with every point a matrix. Link to comment Share on other sites More sharing options...
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