A(A^T)=(A^T)A =I(Identity Matrix)
Then A always have real enteries.
Is it true?
A(A^T)=(A^T)A. Such matrices are called normal
Normal matrix - Wikipedia
If A(A^T)=(A^T)A=E (identity matrix) then A is called orthogonal. A can be defined over the field C of complex numbers, hence, complex entries are admissible
I am asking about the matrix
A(A^T)=(A^T)A=I (identity matrix).
Orthogonal matrix.
Traditionally a matrix A is called orthogonal (rarely, orthonormal ) if A(A^T)=(A^T)A=I (identity matrix).OK. Aniway, it's a question of terminology. Such a matrix A can be real, complex, more generally it can be defined over a field F. The group O(n,F) is the group of all orthogonal matrices of order n over F.
Dear Jogendra Kumar, would you like to make a correction in your original question: you have typed A(A^T)=(A^T)A, not A(A^T)=(A^T)A=I.
@Yuri S Semenov
I am asking about the matrix
A(A^T)=(A^T)A=I (identity matrix).
Orthogonal matrix.
@Peter Breuer
Your ideas of counter examples are impressive.
with best regards
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