Are there any theorems or special properties about the determinant of a matrix representation of an isomorphic linear transformation?
2026-03-27 00:05:12.1774569912
Determinant of the matrix representation of an isomorphic linear transformation
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For a linear transformation, being an isomorphism means exactly being invertible. A linear transformation is invertible if and only if any matrix corresponding to it is invertible.
A matrix is invertible if and only if its determinant is not zero.
Therefore, a linear transformation is an isomorphism if and only if any matrix corresponding to it has non-zero determinant.