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root | A Wisdom Archive on root |  | root A selection of articles related to root |  |
| We recommend this article: root - 1, and also this: root - 2. |
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More material related to Root can be found here:
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root, Root, Root - External link, Root - Root growth, Root - Root structure, Root - Rooting depths, Root - Types of roots, Root - Specialized roots, Rhizophilous - organisms which thrive in a proximity or in a symbiotic relationship with plant roots., Mycorrhiza - root symbiosis in which individual hyphae extending from the mycelium of a fungus colonize the roots of a host plant., fibrous root system, stolon
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ARTICLES RELATED TO root | |
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 |  |  | root: Encyclopedia II - Root - Root growthEarly root growth is a function of the apical meristem located near the tip of the root. The meristem cells more or less continuously divide, producing more meristem, root cap cells (these sacrificed to protect the meristem), and undifferentiated root cells. The latter will become the primary tissues of the root, first undergoing elongation, a process that pushes the root tip forward in the growing medium. Gradually these cells differentiate and mature into sp ...
See also:Root, Root - Root structure, Root - Root growth, Root - Types of roots, Root - Specialized roots, Root - Rooting depths, Root - External link Read more here: » Root: Encyclopedia II - Root - Root growth |
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 |  |  | root: Encyclopedia II - The Roots - Recording historyThe Roots' debut album, Organix, was actually a live recording from a concert in Germany that the Roots sold at their shows. The album earned enough industry buzz to earn the Roots offers from major record labels, and they signed with DGC records, which at the time was better known for its grunge music releases.
The Roots' first album for DGC, Do You Want More?!!!??! (recorded live without the use of samples), was a moderate hit on alternative radio. Their 1996 release Illadelph Halflife was the group's first albu ...
See also:The Roots, The Roots - Members, The Roots - Recording history, The Roots - Awards & Honors, The Roots - Discography Read more here: » The Roots: Encyclopedia II - The Roots - Recording history |
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 |  |  | root: Encyclopedia II - Root of unity - ExamplesThere is only one first root of unity, equal to 1.
The second roots of unity are +1 and -1, of which only -1 is primitive.
The third roots of unity are
where i is the imaginary unit; the latter two roots are primitive.
The fourth roots of unity are
of which + i and See also:Root of unity, Root of unity - Definition, Root of unity - Primitive roots, Root of unity - Examples, Root of unity - Summation, Root of unity - Orthogonality, Root of unity - Omega notation, Root of unity - Cyclotomic polynomials, Root of unity - Cyclotomic fields Read more here: » Root of unity: Encyclopedia II - Root of unity - Examples |
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 |  |  | root: Encyclopedia II - Root of unity - OrthogonalityOne can use the summation formula to prove an orthogonality relationship:
where δ is the Kronecker delta.
The nth roots of unity can be used to form an matrix whose (j,k)th entry is
From above, the columns of this matrix are orthonormal and thus the matrix is unitary. In fact, this matrix is precisely the discrete Fourier transform (alt ...
See also:Root of unity, Root of unity - Definition, Root of unity - Primitive roots, Root of unity - Examples, Root of unity - Summation, Root of unity - Orthogonality, Root of unity - Omega notation, Root of unity - Cyclotomic polynomials, Root of unity - Cyclotomic fields Read more here: » Root of unity: Encyclopedia II - Root of unity - Orthogonality |
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 |  |  | root: Encyclopedia II - Root of unity - SummationAs long as n is at least 2, the nth roots of unity add up to 0. This fact arises in many areas of mathematics and can be proved in a number of ways. One elementary proof is to apply the formula for a geometric series:
Yet another reason for the zero summation is that the roots of unity, plotted in the complex plane, form the vertices of a regular polygon whose b ...
See also:Root of unity, Root of unity - Definition, Root of unity - Primitive roots, Root of unity - Examples, Root of unity - Summation, Root of unity - Orthogonality, Root of unity - Omega notation, Root of unity - Cyclotomic polynomials, Root of unity - Cyclotomic fields Read more here: » Root of unity: Encyclopedia II - Root of unity - Summation |
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 |  |  | root: Encyclopedia II - Rusted Root - HistoryRusted Root was born in 1992 with their indie debut Cruel Sun, which was rereleased in 2002. Their main-label debut album was 1994's When I Woke, a hit on college radio and platinum record. the album's title track hit the top 40 in early 1995, peaking at #33. Along with their increasingly well-known live shows, Rusted Root began working on contributions to the movies Twister and Home for the Holidays. Their next studio album was Remember (1996), followed by Rusted Root (1998) and Welcome to My Party ...
See also:Rusted Root, Rusted Root - Members, Rusted Root - History, Rusted Root - Current situation, Rusted Root - Discography, Rusted Root - Albums, Rusted Root - EPs Read more here: » Rusted Root: Encyclopedia II - Rusted Root - History |
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