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I have been trying to find orthogonal matrix of order n where first row will be given as 1/√n, 1/√n, .... n times.

The second row will be a vector such that dot product of it with the row above and below will be zero and so on. Means, in a matrix of order 3, the 3rd row will be the cross product of first 2 rows.

How do I approach such a problem?

Doc Brown
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The Doctor
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1 Answers1

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Extend the given row vector with n-1 vectors forming a set of n linear independent vectors. For example, 

(1,0,0,...,0,0), 
(0,1,0,...,0,0),
...
(0,0,0,...,1,0),

should be sufficient. Afterwards, you apply the Gram-Schmidt process to these vectors. Since Gram-Schmidt keeps the first vector unchanged, the result will be n orthogonal row vectors, forming the orthogonal matrix you are looking for.

Doc Brown
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