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
<Jeremy Cummings, Other Science>