Proof That Trace Equals Sum of Eigenvalues
A short proof that the trace of a (finite-dimensional) matrix is equal to the sum of its eigenvalues.
Linear Algebra
Proof That Determinant Equals Product of Eigenvalues
A short proof that the determinant of a (finite-dimensional) matrix is equal to the product of its eigenvalues.
Proof of Determinant Additivity From Homogeneity and Column Invariance
A proof of the additivity of determinants from homogeneity and invariance under linear combinations of other columns.