Suppose a square matrix A is diagonalizable. Can this diagonalization necessarily be done by a matrix P with determinant 1?
2025-01-13 07:50:26.1736754626
Suppose A is diagonalizable. Can this diagonalization necessarily be done by a matrix P in the special linear group?
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Just divide one column of $P$ by its determinant.
This argument shows a more general fact: $SL_n$ acts transitively on each $GL_n$-orbit (if the field is algebraically closed as pointed out in the comments)