# Alice and Jacobi in Determinantland

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This Demonstration shows how to calculate the determinant of a generic square matrix by an alternative method to the classic Laplace expansion. The starting point is Jacobi's theorem, which condenses an matrix into an matrix, where .

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Contributed by: D. Meliga and S. Z. Lavagnino (October 2018)

Additional contributions by: F. Mandirola

Open content licensed under CC BY-NC-SA

## Details

Snapshot 1: lowering the dimension by one through the determinant of several square matrices

Snapshot 2: lowering the dimension from a square matrix to a square matrix; in this case only one step is needed to find the determinant

Snapshot 3: lowering the dimension from a square matrix to a square matrix; in this case there are three steps left to find the determinant

References

[1] D. M. Bressoud, *Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture*, New York: Cambridge University Press, 1999.

[2] A. Rice and E. Torrence, "Lewis Carroll’s Condensation Method for Evaluating Determinants," *Math Horizons*, 14(2), 2006 pp. 12–15. (Aug 29, 2018) www.maa.org/sites/default/files/pdf/upload_library/22/Evans/Horizons-Nov06-p12-15.pdf.

## Snapshots

## Permanent Citation