For a given positive integer n, find all non-negative integers r such that the following statement holds:
For any real n×n matrix A with rank r, there exists a real n×n matrix B such that det.
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For a given positive integer n, find all non-negative integers r such that the following statement holds:
For any real n×n matrix A with rank r, there exists a real n×n matrix B such that det.
Let A, B be n \times n Hermitian matrices. Find all positive integer n such that the following statement holds:
“If AB – BA is singular, then A and B have a common eigenvector.”