lamphun Posted August 16, 2006 Share Posted August 16, 2006 Yes it cured my insomnia. Link to comment Share on other sites More sharing options...
suegha Posted August 16, 2006 Share Posted August 16, 2006 It is all about having THE LAST WORD (I think I have recently killed 2 threads by not needing to .... have .... THE LAST WORD) The point here was NOT to have the last word. Isn't is funny how threads sort of become merged, even though they are in different forums? OR Isn't it funny how some posters miss the point? Funny HAHA funny or Funny ironic funny? Funny ironic! Link to comment Share on other sites More sharing options...
daleyboy Posted August 16, 2006 Share Posted August 16, 2006 Good Read. Thanks I couldnt be arsed to read it, you wanna summarise it for us lazy boys? Link to comment Share on other sites More sharing options...
~G~ Posted August 16, 2006 Share Posted August 16, 2006 Many times I find a thread and I respond to it, only to find that I am the last person to respond to it, and it was very active before I got there. It's simple, you're a Llort. (The exact oposite of a Troll) Link to comment Share on other sites More sharing options...
kayo Posted August 16, 2006 Share Posted August 16, 2006 Actually the exact opposite is not Llort, but llorT , but I´m just being picky Link to comment Share on other sites More sharing options...
thaibebop Posted August 17, 2006 Author Share Posted August 17, 2006 Good Read. Thanks I couldnt be arsed to read it, you wanna summarise it for us lazy boys? Sure Bullsht Your welcome. Link to comment Share on other sites More sharing options...
suegha Posted August 17, 2006 Share Posted August 17, 2006 Good Read. Thanks I couldnt be arsed to read it, you wanna summarise it for us lazy boys? Sure Bullsht Your welcome. This thread will never die!?! Link to comment Share on other sites More sharing options...
thaibebop Posted August 17, 2006 Author Share Posted August 17, 2006 Good Read. Thanks I couldnt be arsed to read it, you wanna summarise it for us lazy boys? Sure Bullsht Your welcome. This thread will never die!?! No, it is immortal. Link to comment Share on other sites More sharing options...
suegha Posted August 17, 2006 Share Posted August 17, 2006 Good Read. Thanks I couldnt be arsed to read it, you wanna summarise it for us lazy boys? Sure Bullsht Your welcome. This thread will never die!?! No, it is immortal. Thread everlasting! Link to comment Share on other sites More sharing options...
thaibebop Posted August 17, 2006 Author Share Posted August 17, 2006 Good Read. Thanks I couldnt be arsed to read it, you wanna summarise it for us lazy boys? Sure Bullsht Your welcome. This thread will never die!?! No, it is immortal. Thread everlasting! Like chewing gum. Link to comment Share on other sites More sharing options...
daleyboy Posted August 18, 2006 Share Posted August 18, 2006 Good Read. Thanks I couldnt be arsed to read it, you wanna summarise it for us lazy boys? Sure Bullsht Your welcome. Thought thats what it was about Thanks Link to comment Share on other sites More sharing options...
Khun Yak Posted August 18, 2006 Share Posted August 18, 2006 Good Read. Thanks I couldnt be arsed to read it, you wanna summarise it for us lazy boys? Sure Bullsht Your welcome. Thought thats what it was about Thanks Was it? Link to comment Share on other sites More sharing options...
rishi Posted August 19, 2006 Share Posted August 19, 2006 sigh Link to comment Share on other sites More sharing options...
redrus Posted August 19, 2006 Share Posted August 19, 2006 (edited) sign .........are you the the chosen one................... redrus Edited August 19, 2006 by redrus Link to comment Share on other sites More sharing options...
rishi Posted August 19, 2006 Share Posted August 19, 2006 ... unfortunately not, obviously. Link to comment Share on other sites More sharing options...
Cigarette Burn Posted August 19, 2006 Share Posted August 19, 2006 ? Link to comment Share on other sites More sharing options...
kayo Posted August 19, 2006 Share Posted August 19, 2006 42 Link to comment Share on other sites More sharing options...
Lacoste Posted August 19, 2006 Share Posted August 19, 2006 43 Link to comment Share on other sites More sharing options...
Cigarette Burn Posted August 19, 2006 Share Posted August 19, 2006 (edited) At the far right are several large areas of activity in numerical linear algebra and related topics, typically, the study of individual matrices or transformations between (large-dimensional) real vector spaces. Numerical linear algebra per se (e.g. the determination of fast methods of solving thousands of simultaneous linear equations, the stability of eigenvalue calculations, applications to finite-element methods, sparse matrix techniques) are parts of 65: Numerical Analysis, particularly 65F: Numerical linear algebra. Here we include several fields of inquiry into the underlying linear systems and their applications. In this category we might include 15A06: Linear equations, 15A09: Matrix inversion and generalized inverses, 15A18: Eigenvalues and singular values, 15A23: Factorization of matrices (SVD, LU, QR, etc.), 15A12: Conditioning of matrices, as well as applications to physics (15A90), Control Theory (93) and Statistics (62) such as what is there known as Principal Component Analysis. Related topics include those of importance in 90: Operations Research (especially linear programming) such as 15A48: Positive matrices, 15A39: Linear inequalities, and 15A45: Miscellaneous matrix inequalities. The circles in shades of red in the lower part of the graph show connections with other fields of algebra. Furthest down is 15A72: Invariant theory and tensor algebra, which crosses to the study of invariants in Group Theory (20) and in polynomial rings (13: Commutative Algebra and 14: Algebraic Geometry). Certain sets of matrices form well-known groups, particularly the Lie groups (22) and algebraic groups. Closer to the center of the picture are connections with Number Theory (10 and 11), especially 15A63: Quadratic forms. There are several connections with ring theory (16: Noncommutative Rings, 17: Nonassociative Rings, 19: Algebraic K-Theory); indeed many of the key examples of such rings involve collections of matrices, including the full matrix rings and Lie rings, and rings of matrices are used for representing groups and general rings. Related disciplines within Linear Algebra include 15A27: Commutativity, 15A30: Algebraic systems of matrices, 15A33: Matrices over special rings (including 12: Fields), 15A36: Matrices of integers, 15A75: Grassmann algebras, and 15A78: Other algebras. Tensor products in linear algebra (15A69) mirror such constructs in other algebraic categories. Nearby are several fields in discrete mathematics, including the use of matrices for the representation of combinatorical objects such as graphs (05: Combinatorics), extremal matrices, permanents (15A15), and applications to 68:Computer Science, 94: Information Theory (e.g. linear codes), and 39: Difference equations. In the upper left are the papers in "geometric algebra", including 15A66 (Clifford algebras), 81 (Quantum theory), 53 (Differential Geometry), and 58 (Analysis on manifolds). In the upper right are the topics appropriate for 60: Probability and 62: Statistics, including 15A51: Stochastic matrices and 15A52: Random matrices, and applications to statistical mechanics (82) and the sciences (92). Linear maps of geometric interest are considered in the geometry pages (51, 52). For example, rotation matrices and affine changes of coordinates come under 51F15. Sets of matrices qua sets arise geometrically as well; for example certain families of matrices form manifolds, and even topological groups (22). Subfields There is only one division (15A) but it is subdivided: 15A03: Vector spaces, linear dependence, rank 15A04: Linear transformations, semilinear transformations 15A06: Linear equations 15A09: Matrix inversion, generalized inverses 15A12: Conditioning of matrices, See also 65F35 15A15: Determinants, permanents, other special matrix functions, See also 19B10, 19B14 15A18: Eigenvalues, singular values, and eigenvectors 15A21: Canonical forms, reductions, classification 15A22: Matrix pencils, See also 47A56 15A23: Factorization of matrices 15A24: Matrix equations and identities 15A27: Commutativity 15A29: Inverse problems [new in 2000] 15A30: Algebraic systems of matrices, See also 16S50, 20Gxx, 20Hxx 15A33: Matrices over special rings (quaternions, finite fields, etc.) 15A36: Matrices of integers, See also 11C20 15A39: Linear inequalities 15A42: Inequalities involving eigenvalues and eigenvectors 15A45: Miscellaneous inequalities involving matrices 15A48: Positive matrices and their generalizations; cones of matrices 15A51: Stochastic matrices 15A52: Random matrices 15A54: Matrices over function rings in one or more variables 15A57: Other types of matrices (Hermitian, skew-Hermitian, etc.) 15A60: Norms of matrices, numerical range, applications of functional analysis to matrix theory, See also 65F35, 65J05 15A63: Quadratic and bilinear forms, inner products See mainly 11Exx 15A66: Clifford algebras, spinors 15A69: Multilinear algebra, tensor products 15A72: Vector and tensor algebra, theory of invariants, See Also 13A50, 14D25 15A75: Exterior algebra, Grassmann algebras 15A78: Other algebras built from modules 15A90: Applications of matrix theory to physics 15A99: Miscellaneous topics Though I agree with your theory you also have to take in to account the modern setting for differential equations and global analysis. Most of the study of linear algebra in these infinite-dimensional (i.e. topological) spaces is classified separately in the fields of functional analysis including: Function Analysis proper, Abstract harmonic analysis, and Operator theory. Here we are concerned with similar perspectives with interesting consequences even for finite-dimensional spaces. In particular one might include 15A60: Matrix norms, 15A57: Hermitian and other classes of matrices, 15A24: Matrix equations and identities, 15A54: Matrices over function rings in one or more variables, 15A42: Inequalities involving eigenvalues, and 15A22: Matrix pencils. Just a thought. Edited August 19, 2006 by Cigarette Burn Link to comment Share on other sites More sharing options...
kayo Posted August 19, 2006 Share Posted August 19, 2006 doñt think anymore. please. Link to comment Share on other sites More sharing options...
thaibebop Posted August 19, 2006 Author Share Posted August 19, 2006 ooooooohhhhhhhh Head hurts. Link to comment Share on other sites More sharing options...
Khun Yak Posted August 19, 2006 Share Posted August 19, 2006 doñt think anymore. please. I may second that... ...if I may Link to comment Share on other sites More sharing options...
kayo Posted August 20, 2006 Share Posted August 20, 2006 You may not, but you are rather august Link to comment Share on other sites More sharing options...
Jockstar Posted August 20, 2006 Share Posted August 20, 2006 You may not, but you are rather august Eh? Link to comment Share on other sites More sharing options...
raro Posted August 21, 2006 Share Posted August 21, 2006 Kayo is weird! Now everybody: Kayo is a wacko! Kayo is a wacko! Kayo is a wacko! Link to comment Share on other sites More sharing options...
daleyboy Posted August 21, 2006 Share Posted August 21, 2006 Kayo is a wacko! Kayo is a wacko! Kayo is a wacko! Link to comment Share on other sites More sharing options...
kayo Posted August 21, 2006 Share Posted August 21, 2006 Kayo is a wacko! Kayo is a wacko! Kayo is a wacko! Link to comment Share on other sites More sharing options...
jimmy5L Posted August 22, 2006 Share Posted August 22, 2006 ?????????? Can somebody tell me what's going on! (don't wanne read all the 20 pages!) Link to comment Share on other sites More sharing options...
thaibebop Posted August 22, 2006 Author Share Posted August 22, 2006 Echo? Link to comment Share on other sites More sharing options...
kayo Posted August 22, 2006 Share Posted August 22, 2006 Echo Echo Wakko Kayo Link to comment Share on other sites More sharing options...
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