SU(2) and Complex Rotations

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I was reading about SU(2) in a physics book and I had a question about the rotations it represents. I was told that a matrix in SU(2) would preserve the magnitude of a 2-dimensional complex vector. It seemed to be implied in the book that this was an if and only if relationship, but from what I can tell multiplying a vector by a matrix with unit-length complex numbers on the diagonal and zeroes elsewhere should also preserve the magnitude. However, such a matrix doesn’t seem to be a member of SU(2). I must be missing something here but I can’t tell what it is. Thanks!




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    I was reading about SU(2) in a physics book and I had a question about the rotations it represents. I was told that a matrix in SU(2) would preserve the magnitude of a 2-dimensional complex vector. It seemed to be implied in the book that this was an if and only if relationship, but from what I can tell multiplying a vector by a matrix with unit-length complex numbers on the diagonal and zeroes elsewhere should also preserve the magnitude. However, such a matrix doesn’t seem to be a member of SU(2). I must be missing something here but I can’t tell what it is. Thanks!




    linear-algebra complex-numbers linear-transformations




    share|cite|improve this question





















      up vote
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      up vote
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      down vote

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      I was reading about SU(2) in a physics book and I had a question about the rotations it represents. I was told that a matrix in SU(2) would preserve the magnitude of a 2-dimensional complex vector. It seemed to be implied in the book that this was an if and only if relationship, but from what I can tell multiplying a vector by a matrix with unit-length complex numbers on the diagonal and zeroes elsewhere should also preserve the magnitude. However, such a matrix doesn’t seem to be a member of SU(2). I must be missing something here but I can’t tell what it is. Thanks!




      linear-algebra complex-numbers linear-transformations




      share|cite|improve this question











      I was reading about SU(2) in a physics book and I had a question about the rotations it represents. I was told that a matrix in SU(2) would preserve the magnitude of a 2-dimensional complex vector. It seemed to be implied in the book that this was an if and only if relationship, but from what I can tell multiplying a vector by a matrix with unit-length complex numbers on the diagonal and zeroes elsewhere should also preserve the magnitude. However, such a matrix doesn’t seem to be a member of SU(2). I must be missing something here but I can’t tell what it is. Thanks!





      linear-algebra complex-numbers linear-transformations





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      asked Jul 18 at 23:18









      Andres Cook

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