In linear algebra, a symmetric formula_1 real matrix formula_2 is said to be positive-definite if the scalar formula_3 is strictly positive for every non-zero column vector formula_4 of formula_5 real numbers. Here formula_6 denotes the transpose of When interpreting formula_7 as the output of an operator, that is acting on an input, the property of positive definiteness implies that the output always has a positive inner product with the input, as often observed in physical processes. Put differently, formula_7 is in the general direction of formula_4 (within an angle of formula_10 of