Editing Cholesky decomposition (section)

===Kalman filters===
[[Unscented Kalman filter]]s commonly use the Cholesky decomposition to choose a set of so-called sigma points.  The Kalman filter tracks the average state of a system as a vector {{math|'''x'''}} of length {{mvar|N}} and covariance as an {{math|''N'' × ''N''}} matrix {{math|'''P'''}}.  The matrix {{math|'''P'''}} is always positive semi-definite and can be decomposed into '''LL'''<sup>T</sup>.  The columns of {{math|'''L'''}} can be added and subtracted from the mean {{math|'''x'''}} to form a set of {{math|2''N''}} vectors called ''sigma points''.  These sigma points completely capture the mean and covariance of the system state.