Task: Text Categorization
Input (English): When using differentiable functions in classic Sturm-Liouville problems, these quantities are real and may be ordered to form an infinite sequence. When Markov, or stochastic, processes are represented as a collection of probability column vectors, these quantities must include 1 among their number. The determinant of a triangular matrix equals the product of these quantities, which can be found in some matrix A by solving the characteristic polynomial in terms of some variable, obtained when subtracting that variable times the identity matrix from A. FTP, identify these scalars, usually identified as lambda, which solve, for some vector x, A times x equals lamda times x.
Output (English): Science