In mathematics, Hurwitz determinants were introduced by Adolf Hurwitz (1895), who used them to give a criterion for all roots of a polynomial to have...

compute the Hurwitz determinants ( Δ i {\displaystyle \Delta _{i}} ) than computing them directly. A polynomial satisfying the Routh–Hurwitz criterion is...

Adolf Hurwitz. Edited by Peter Ullrich. Vieweg, Braunschweig 1988, ISBN 3-528-06334-3. First Hurwitz triplet Hurwitz class number Hurwitz determinant Hurwitz-stable...

is called Hurwitz determinants. Their definition is related to the associated Hurwitz matrix. Proposition 1. If all the Hurwitz determinants c i , 0 {\displaystyle...

The minors Δ k ( p ) {\displaystyle \Delta _{k}(p)} are called the Hurwitz determinants. Similarly, if a 0 < 0 {\displaystyle a_{0}<0} then the polynomial...

s , a ) {\displaystyle \zeta _{H}(s,a)} is the Hurwitz zeta function. We will compute the determinant of the following operator describing the motion...

where a = ‖ C 2 h ‖ 2 {\displaystyle a=\Vert C_{2}h\Vert _{2}} . Hurwitz determinant Strang, Gilbert (1996). "Eigenvalues of ( ↓ 2 ) H {\displaystyle...

numbers; the other being the complex numbers. These rings are also Euclidean Hurwitz algebras, of which the quaternions are the largest associative algebra...

over V and SZ(V) is the subgroup of scalar transformations with unit determinant. Here SZ is the center of SL, and is naturally identified with the group...

proved that if a Z-matrix has all of its row sums positive, then the determinant of that matrix is positive. An M-matrix is commonly defined as follows:...

doi:10.1090/s0002-9904-1912-02210-3. MR 1559206. Hurwitz, W. A. (1914). "Note on the Fredholm determinant". Bull. Amer. Math. Soc. 20 (8): 406–408. doi:10...

However, the real determinant of multiplication by a complex number α equals |α|2, so the Jacobian of h has positive determinant. Consequently, the complex...

feedback. Psychonomic Science,20,282-285. Hurwitz, H.M.B., & Roberts, A.E. (1971). Time-out as a determinant of rate of response and rate of avoidance...

structure to the determinant formula for the normal cross product in R3 except that the row of basis vectors is the last row in the determinant rather than...

7 elements. These have nonzero determinant. The subgroup SL(2, 7) consists of all such matrices with unit determinant. Then PSL(2, 7) is defined to be...

advantage over the Routh–Hurwitz criterion because it involves only about half the number of determinant computations. The Routh–Hurwitz stability criterion...

× 2 {\displaystyle 2\times 2} matrices with integer coefficients and determinant 1 {\displaystyle 1} , such that the matrices A {\displaystyle A} and...

1857 and named after Étienne Bézout. Bézoutian may also refer to the determinant of this matrix, which is equal to the resultant of the two polynomials...

1933, though its special case for Lie groups had been introduced by Adolf Hurwitz in 1897 under the name "invariant integral". Haar measures are used in...

(n)\quad {\text{ for }}(m,n)=1.} The idea goes back to earlier work of Adolf Hurwitz, who treated algebraic correspondences between modular curves which realise...

identically zero. The restriction to 0, 1, 3 and 7 dimensions is related to Hurwitz's theorem, that normed division algebras are only possible in 1, 2, 4 and...

that π can be obtained from the functional determinant of the harmonic oscillator. This functional determinant can be computed via a product expansion,...

Interactions". mBio. 8 (4). doi:10.1128/mBio.00893-17. PMC 5513705. PMID 28698277. Hurwitz, B. L.; Westveld, A. H.; Brum, J. R.; Sullivan, M. B. (2014). "Modeling...

auxiliary valuation function. When f {\displaystyle f} has a Jacobian determinant | J | {\displaystyle |J|} , then g {\displaystyle g} is usually taken...

Riemann surfaces, and enumeration of branched coverings, or so-called Hurwitz numbers. There are two notions of τ {\displaystyle \tau } -functions, both...

all normed division algebras over R {\displaystyle \mathbb {R} } . By Hurwitz's theorem they are the only ones; the sedenions, the next step in the Cayley–Dickson...

that fall between these two extremes. Culwell KR, Vekemans M, de Silva U, Hurwitz M, Crane BB (July 2010). "Critical gaps in universal access to reproductive...

it is no longer bilinear. These identities are strongly related with Hurwitz's classification of composition algebras. The Brahmagupta–Fibonacci identity...

1002/14651858.CD010283.pub2. PMC 10772940. PMID 25080126. Teoh L, Cates CJ, Hurwitz M, Acworth JP, van Asperen P, Chang AB (April 2012). "Anticholinergic therapy...

1176/appi.ajp.2012.12030301. PMID 23223893. Lambert CG, Mazurie AJ, Lauve NR, Hurwitz NG, Young SS, Obenchain RL, et al. (May 2016). "Hypothyroidism risk compared...