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Rudhreswaran G posted an Question
July 11, 2021 • 13:45 pm
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30 points
30 points
- IIT JAM
- Mathematics (MA)
Can some one explain the below two points ?
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Ankur Rao![best-answer]()
Orthogonal matrix This is a matrix where the product of the matrix and its transpose is the identity matrix, i.e. A x At = At x A = I (At being the transpose - swapping rows and columns of the matrix along the main diagonal) A unitary matrix: This is a matrix where the product of the matrix with its complex conjugate transpose is the identity matrix, i.e. A x At* = At* x A = I (where At* is the complex conjugate of At - take complex conjugate of each element of At) For a real number system At = At*, so both would be the same, since complex conjugate of a real number is the number itself. In Orthogonal Matrix and unitary matrix the dot product of a column (row) with other column (row) is zero and when we find distance of each column (row) it will be 1. feel free to ask if you have any doubts.