Task: Text Categorization
Input (English): These entites are bounded in a spectrum according to the Gershgorin circle theorem. John Francis and Vera Kublanovskaya formulated the QR algorithm for these entities, whose corresponding qualitative theory in the Sturm-Liouville theory. Rayleigh quotient iteration extends inverse iteration and converges to them cubically, while multiple rotations are used to obtain a (*) diagonal approximating these entities in the Jacobi algorithm. The Lanczos algorithm uses power methods to calculate these entities, which can be used to characterize the stability of solutions to ODEs. The sum of these values and the product of these values equal a matrix's trace and a matrix's determinant respectively. FTP, name these solutions to a characteristic equation, which are special sets of scalars associated with the invariants of a linear system of equations.
Output (English): Science