The Characteristic Values and the Standard Form of a Quadratic Form Represented with a Real Symmetrical Determinant
Dalin Li · 2004
Let the characteristic values of a n order real symmetrical matrix B be λ_1,λ_2,…,λ_n. The characteristic values of the quadratic form BX~T X0 are λ′_i=-∏nk=1且k≠iλ_k. BX~T X0can be simplified to CY~T Y0 by the diagonalizable orthogonal transformation X~T=PY~T of B. Here C is diag(λ_1,λ_2,…,λ_n).