Succinct data structure - Revision history

en>Nbarth: /* Examples */ strings

2014-11-23T21:36:56Z

Examples: strings

← Older revision		Revision as of 23:36, 23 November 2014
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	~~Nice to satisfy you, my title is Araceli Oquendo but~~ I ~~don~~'~~t like when individuals use my complete title~~. ~~Bookkeeping has been his working day job for a whilst~~. ~~He presently lives in Idaho and his mothers and fathers live nearby~~. The ~~thing~~ I ~~adore most flower arranging and now~~ I ~~have time to take on new issues~~.<br><br>my ~~page -~~ [http://~~Exitus~~.~~bplaced.net~~/index.php?mod=users&action=view&id=~~139 car warranty~~]		I'm Yoshiko Oquendo. Arizona is her birth place and she will never move. To maintain birds is 1 of the things he enjoys most. The job I've been occupying for many years is a bookkeeper but I've already applied for an additional one.<br><br>Visit my blog: [http://muehle-Kruskop.de/index.php?mod=users&action=view&id=22344 http://muehle-Kruskop.de]

en>NovaDenizen: Fixed rank definition

2014-02-12T18:25:23Z

Fixed rank definition

← Older revision		Revision as of 20:25, 12 February 2014
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	~~{{Unreferenced\|date=February 2008}}~~		Nice to satisfy you, my title is Araceli Oquendo but I don't like when individuals use my complete title. Bookkeeping has been his working day job for a whilst. He presently lives in Idaho and his mothers and fathers live nearby. The thing I adore most flower arranging and now I have time to take on new issues.<br><br>my page - [http://Exitus.bplaced.net/index.php?mod=users&action=view&id=139 car warranty]
	~~The ''~~'~~[[tensor product]] of [[quadratic form]]s''' is most easily understood~~ when ~~one views the quadratic forms as ''[[quadratic space]]s''~~. ~~So, if (''V'', ''q''<sub>1</sub>) and (''W'', ''q''<sub>2</sub>) are quadratic spaces, with ''V'',''W'' [[vector spaces]], then the tensor product is~~ a ~~quadratic form ''q'' on the [[Tensor product#Tensor product of vector spaces\|tensor product of vector spaces]] ''V'' ⊗ ''W''~~.

	~~It is defined~~ in ~~such a way that for <math>v \otimes w \in V \otimes W</math> we~~ have <~~math~~>~~q(v \otimes w) = q_1(v)q_2(w)~~<~~/math~~>~~. In particular, if we have diagonalizations of our quadratic forms (which is always possible when the~~ [~~[characteristic (algebra)\|characteristic]] is not 2) such that~~

	:~~<math>q_1 \cong \langle a_1, .~~.. ~~, a_n \rangle<~~/~~math>~~
	~~:<math>q_2 \cong \langle b_1,~~ .~~.. , b_m \rangle</math>~~

	~~then the tensor product has diagonalization~~

	~~:<math>q_1 \otimes q_2~~ = ~~q \cong \langle a_1b_1, a_1b_2, ... a_1b_m, a_2b_1, ... , a_2b_m , ... , a_nb_1, ... a_nb_m \rangle.</math>~~

	~~[[Category:Quadratic forms~~]]
	~~[[Category:Tensors]]~~

	~~{{algebra-stub}}~~

en>Tobias Bergemann: Missing word.

2013-12-28T10:56:01Z

Missing word.

← Older revision		Revision as of 12:56, 28 December 2013
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	The ~~name~~ of the ~~writer~~ is ~~Garland~~. ~~Playing crochet~~ is a ~~thing~~ that ~~I'm totally addicted to. For years she's been living~~ in ~~Kansas~~. ~~Managing individuals~~ is ~~how she tends to make money and she will~~ not ~~alter it whenever quickly~~.<br><br>~~My page [http://www~~.~~shownetbook~~.~~com~~/~~enone/xe/?document_srl~~=~~3029968 http://www~~.~~shownetbook~~.~~com~~/~~enone/xe/?document_srl=3029968~~]		{{Unreferenced\|date=February 2008}}
			The '''[[tensor product]] of [[quadratic form]]s''' is most easily understood when one views the quadratic forms as ''[[quadratic space]]s''. So, if (''V'', ''q''<sub>1</sub>) and (''W'', ''q''<sub>2</sub>) are quadratic spaces, with ''V'',''W'' [[vector spaces]], then the tensor product is a quadratic form ''q'' on the [[Tensor product#Tensor product of vector spaces\|tensor product of vector spaces]] ''V'' ⊗ ''W''.

			It is defined in such a way that for <math>v \otimes w \in V \otimes W</math> we have <math>q(v \otimes w) = q_1(v)q_2(w)</math>. In particular, if we have diagonalizations of our quadratic forms (which is always possible when the [[characteristic (algebra)\|characteristic]] is not 2) such that

			:<math>q_1 \cong \langle a_1, ... , a_n \rangle</math>
			:<math>q_2 \cong \langle b_1, ... , b_m \rangle</math>

			then the tensor product has diagonalization

			:<math>q_1 \otimes q_2 = q \cong \langle a_1b_1, a_1b_2, ... a_1b_m, a_2b_1, ... , a_2b_m , ... , a_nb_1, ... a_nb_m \rangle.</math>

			[[Category:Quadratic forms]]
			[[Category:Tensors]]

			{{algebra-stub}}

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-11T16:47:55Z

ISBNs (Build KE)

New page

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