[math-fun] Consequential zero entries in an orthogonal matrix
A denotes a 5x5 orthogonal matrix, with A_21 = A_31 = A_43 = A_53 = 0 ; why should necessarily A_13 = 0 also? Generalise ... ?? WFL
For columns 1 and 3 to be orthogonal, and your zero-values, the product of A_11 and A13 must be zero — so at least one of them is zero. Am I missing something? -Veit
On May 23, 2016, at 11:47 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
A denotes a 5x5 orthogonal matrix, with A_21 = A_31 = A_43 = A_53 = 0 ; why should necessarily A_13 = 0 also?
Generalise ... ??
WFL
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Duh --- of course --- thanks! The general problem is to characterise explicitly the possible patterns of zeros and nonzero entries which can occur in an orthonormal matrix. As you can see, I'm having trouble keeping track of the large number of possibilities. WFL On 5/23/16, Veit Elser <ve10@cornell.edu> wrote:
For columns 1 and 3 to be orthogonal, and your zero-values, the product of A_11 and A13 must be zero — so at least one of them is zero. Am I missing something?
-Veit
On May 23, 2016, at 11:47 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
A denotes a 5x5 orthogonal matrix, with A_21 = A_31 = A_43 = A_53 = 0 ; why should necessarily A_13 = 0 also?
Generalise ... ??
WFL
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Counter-example? 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 Tom Fred Lunnon writes:
A denotes a 5x5 orthogonal matrix, with A_21 = A_31 = A_43 = A_53 = 0 ; why should necessarily A_13 = 0 also?
Generalise ... ??
WFL
participants (3)
-
Fred Lunnon -
Tom Karzes -
Veit Elser