Various closed form formulas for summing the first n terms of a sequence [itex] \{a_i\} [/itex] of numbers can be developed by considering the various order differences of the terms, such as [itex]{\triangle} a_i = a_{i+1} - a_i [/itex] and [itex] \triangle^2 a_i = \triangle ( \triangle a_i) [/itex]. Closed form formulas occur if the m th and higher order differences of the terms vanish for some m.(adsbygoogle = window.adsbygoogle || []).push({});

If we have a sequence of invertible matrices [itex] \{A_i \} [/itex] can anything interesting be said about finding the product of the first n terms using information about the quotients of consecutive terms? ( [itex] \delta A_i = A_{i+1} A_{i}^{-1} [/itex] )?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Any useful analog to finite differences for matrix products?

Loading...

Similar Threads - useful analog finite | Date |
---|---|

I Solving a system of linear equations using back substitution | Aug 30, 2017 |

I Normal modes using representation theory | Aug 9, 2017 |

I Using determinant to find constraints on equation | Jan 15, 2017 |

A reasonable analogy for understanding similar matrices? | Dec 12, 2015 |

**Physics Forums - The Fusion of Science and Community**