How can I show that the product of two tridiagonal matrix results in a pentadiagonal matrix?
Why is the product of two tridiagonal matrix is a pentadiagonal matrix?
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linear-algebra
1 Answers
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See the following paper: M. Capovani. Su alcune proprietà delle matrici tridiagonali e pentadiagonali.
Su alcune proprietà delle matrici tridiagonali e pentadiagonali.
Capovani proves that the inverse of a nonsymmetric tridiagonal matrix with the super and subdiagonal elements different from zero, also has as inverse a generator representable matrix, where the upper and lower triangular part have different generators. Using these results the author proves that a pentadiagonal matrix can be written as the product of two tridiagonal matrices, for which one of them is symmetric.