Pascal matrix

Pascal matrix

Totally Positive and Totally Nonnegative Matrices

Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006

Observe that the rows of L, or the columns of U, come from the rows of Pascal’s triangle (ignoring the zeros); hence, the name Pascal matrix (see Example 4 for a definition of Pn).

A connection between time domain model order reduction and moment matching for LTI systems

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Journal Information

Published in Mathematical and Computer Modelling of Dynamical Systems, 2018

Manuela Hund, Jens Saak

that is known as the Pascal matrix. It can be shown (see, e.g. [18]) that the LU decomposition of this matrix leads to its triangular factors being triangular Pascal matrices, and thus the determinant is always 1. Consequently, always has full rank and we have established the equivalence to moment matching choosing the expansion points as eigenvalues of , i.e. .

Fibonacci and Lucas Riordan arrays and construction of pseudo-involutions

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Journal Information

Published in Applicable Analysis, 2021

Candice Marshall, Asamoah Nkwanta

A typical example of a Riordan matrix is the Pascal matrix. In this case, and . In pair form notation, where the entries of the Pascal Riordan matrix are Pascal's triangle A007318 [1] written in infinite lower-triangular form.

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Totally Positive and Totally Nonnegative Matrices

A connection between time domain model order reduction and moment matching for LTI systems

Fibonacci and Lucas Riordan arrays and construction of pseudo-involutions