What does zonal polynomial mean?
Definitions for zonal polynomial
zon·al po·ly·no·mi·al
This dictionary definitions page includes all the possible meanings, example usage and translations of the word zonal polynomial.
Wikipedia
Zonal polynomial
In mathematics, a zonal polynomial is a multivariate symmetric homogeneous polynomial. The zonal polynomials form a basis of the space of symmetric polynomials. They appear as zonal spherical functions of the Gelfand pairs ( S 2 n , H n ) {\displaystyle (S_{2n},H_{n})} (here, H n {\displaystyle H_{n}} is the hyperoctahedral group) and ( G l n ( R ) , O n ) {\displaystyle (Gl_{n}(\mathbb {R} ),O_{n})} , which means that they describe canonical basis of the double class algebras C [ H n ∖ S 2 n / H n ] {\displaystyle \mathbb {C} [H_{n}\backslash S_{2n}/H_{n}]} and C [ O d ( R ) ∖ M d ( R ) / O d ( R ) ] {\displaystyle \mathbb {C} [O_{d}(\mathbb {R} )\backslash M_{d}(\mathbb {R} )/O_{d}(\mathbb {R} )]} . They are applied in multivariate statistics. The zonal polynomials are the α = 2 {\displaystyle \alpha =2} case of the C normalization of the Jack function.
Numerology
Chaldean Numerology
The numerical value of zonal polynomial in Chaldean Numerology is: 9
Pythagorean Numerology
The numerical value of zonal polynomial in Pythagorean Numerology is: 2
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"zonal polynomial." Definitions.net. STANDS4 LLC, 2024. Web. 30 Apr. 2024. <https://www.definitions.net/definition/zonal+polynomial>.
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