determinant - 2025 Penn Bowl

Question

This function is used to compute each of the entries in the rth (“arth”) multiplicative compound. For 10 points each:

[10m] Name this function computed for a product by the Cauchy–Binet (“KO-shee-bin-AY”) formula. Laplace names a recursive expansion of this function in terms of cofactors.

ANSWER: determinant [or det]

[10h] This mathematician names a criterion that uses minors to test for positive-definite Hermitian matrices. A quadratic form has constant signature under change of basis by this mathematician’s law of inertia.

ANSWER: James Joseph Sylvester

[10e] Sylvester also names a formula for passing functions of a matrix to these quantities. These elements in a matrix’s spectrum are typically denoted by lambdas.

ANSWER: eigenvalues

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Summary


2025 Penn Bowl - BU	11/01/25	Y	4	22.50	100%	75%	50%
2025 Penn Bowl - CWRU	11/01/25	Y	3	16.67	100%	67%	0%
2025 Penn Bowl - Mainsite (UPenn)	11/01/25	Y	6	15.00	83%	67%	0%
2025 Penn Bowl - Murray State	11/08/25	Y	2	0.00	0%	0%	0%
2025 Penn Bowl - Northwestern	10/25/25	Y	4	15.00	100%	50%	0%
2025 Penn Bowl - Online	11/08/25	Y	2	0.00	0%	0%	0%
2025 Penn Bowl - Ottawa	11/01/25	Y	7	17.14	100%	57%	14%
2025 Penn Bowl - Stanford	10/25/25	Y	4	12.50	100%	0%	25%
2025 Penn Bowl - UK	11/01/25	Y	9	14.44	100%	22%	22%
2025 Penn Bowl - UNC	11/01/25	Y	3	13.33	67%	67%	0%
2025 Penn Bowl - WashU	11/01/25	Y	2	5.00	50%	0%	0%

Data


RIT	Brandeis	10	10	10	30
Yale	Brown	10	0	10	20
I've been running into you in my lead plumbocene what could have benzene	Harvard	0	0	10	10
MIT A	MIT B	10	10	10	30
Michigan B	CWRU	0	0	10	10
Ohio State A	Michigan C	10	0	10	20
Pittsburgh	Ohio State B	10	0	10	20
John Jay	Mount Sinai	10	0	10	20
NYU A	NYU B	0	0	10	10
JHU A	Columbia A	10	0	10	20
Columbia B	Maryland C	0	0	0	0
Maryland A	Swarthmore	10	0	10	20
Maryland B	JHU B	10	0	10	20
Central Oklahoma	Texas A	0	0	0	0
Oklahoma	Texas B	0	0	0	0
Illinois	UChicago C	10	0	10	20
New Young Whigs of America	Wake Up Paddington A Washington Mystery	0	0	0	0
rusty shackleford	abg academy	0	0	0	0
Aweille Kevin Fan osti continue comme ça	Toronto Operation PBSuccess	0	0	10	10
Toronto G	Toronto Sunshine Bubbles	10	0	10	20
Waterloo you are crooked	Carleton A	10	10	10	30
McGill B	Toronto Murder on the Rider Express	10	0	10	20
Queen's is monitoring the situation	McGill Fartlets	0	0	10	10
#OpenToBuzz	Ottawa 67s	10	0	10	20
Guelph perfomative male competition	Toronto E	0	0	10	10
Northwestern A	Indiana	0	0	10	10
Berkeley B	In Search of Lost Clues	0	0	10	10
Berkeley C	Free Win	0	0	10	10
Stanford B	Stanford A	0	0	10	10
Berkeley A	The best time to buzz was twenty clues ago. The second best time to buzz is now	0	10	10	20
Burnaburiash's Lapis Lazuli	1. Wawa 2. Blank Street 151. Black Sheep at Kings Cross rail	10	10	10	30
Washed Scrubs	Galactic Ombudsmen	0	0	10	10
Of Mice and Penn	Chimp Brisket	0	0	10	10
Knorr Stock Clue	Paul Quifford, or, It Was a Dark and Stormy Tournament	0	0	10	10
Penn and the Art of Tossup-Bonus cycle Maintenance	Coughing Baby	10	0	10	20
Bristold	The Bit and the Penndulum	0	0	10	10
To buzz is to be perceived	Hail to the Sheaf	0	10	10	20
Quiztian Bale in Ratman Begins	question mark	0	0	10	10
Alas poor Warwick, I knew him Edinburgh	why is it called a score clue if nobody scores points on it	0	0	10	10
UChicago B	Northwestern B	10	0	10	20
VT B	UNC B	10	0	10	20
VT A	Planck Sinatra	10	0	10	20
UNC A	Wise Duke	0	0	0	0
UChicago A	Purdue B	0	0	10	10
Truman State	WashU Kiki	0	0	0	0
WashU Bouba	VJ Edgecombe School of Interior Design - Edwardsville	0	0	10	10