Abstract
We present a novel perspective on developing the determinant through the lens of signed volume. Starting with a unique and rigorous development of both the volume and orientation of a parallelepiped, we are able to give an unambiguous, basis-free definition for the determinant of a linear transformation. We then build intuition for the determinant by proving many of its properties in a succinct and basis-free fashion. We conclude our journey by using these properties to derive a well-known method for computing the determinant and motivating the Laplace expansion.
Original language | English (US) |
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Pages (from-to) | 437-447 |
Number of pages | 11 |
Journal | American Mathematical Monthly |
Volume | 126 |
Issue number | 5 |
DOIs | |
State | Published - May 28 2019 |
All Science Journal Classification (ASJC) codes
- General Mathematics