- #1

Stephen Tashi

Science Advisor

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## Main Question or Discussion Point

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.

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] )?

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] )?