The determinant of a triangular matrix is the product of the entries on the diagonal.
Created almost 9 years ago, updated 5 months ago
ID23744
Theorem: The determinant of a triangular matrix is the product of the entries on the diagonal: $\det(T) = t_{11} \cdot t_{22} \cdots t_{nn}$. This follows from cofactor expansion or from the fact that the eigenvalues of a triangular matrix are its diagonal entries and $\det(A) = \prod \lambda_i$.
**Theorem:** The determinant of a triangular matrix is the product of the entries on the diagonal: $\det(T) = t_{11} \cdot t_{22} \cdots t_{nn}$. This follows from cofactor expansion or from the fact that the eigenvalues of a triangular matrix are its diagonal entries and $\det(A) = \prod \lambda_i$.