Thread Killer?

[lamphun]

Yes it cured my insomnia.

[suegha]

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!

[daleyboy]

Good Read. Thanks

I couldnt be arsed to read it, you wanna summarise it for us lazy boys?

[~G~]

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)

[kayo]

Actually the exact opposite is not Llort, but llorT , but I´m just being picky

[thaibebop]

Good Read. Thanks

I couldnt be arsed to read it, you wanna summarise it for us lazy boys?

Sure

Bullsht

Your welcome.

[suegha]

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!?!

[thaibebop]

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.

[suegha]

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!

[thaibebop]

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.

[daleyboy]

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

[Khun Yak]

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?

[rishi]

sigh

[redrus]

sign

.........are you the the chosen one...................

redrus

Edited August 19, 2006 by redrus

[rishi]

... unfortunately not, obviously.

[Cigarette Burn]

?

[kayo]

42

[Lacoste]

43

[Cigarette Burn]

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

[kayo]

doñt think anymore. please.

[thaibebop]

ooooooohhhhhhhh Head hurts.

[Khun Yak]

doñt think anymore. please.

I may second that...

...if I may

[kayo]

You may not, but you are rather august

[Jockstar]

You may not, but you are rather august

Eh?

[raro]

Kayo is weird!

Now everybody: Kayo is a wacko! Kayo is a wacko! Kayo is a wacko!

[daleyboy]

Kayo is a wacko! Kayo is a wacko! Kayo is a wacko!

[kayo]

Kayo is a wacko! Kayo is a wacko! Kayo is a wacko!

[jimmy5L]

??????????

Can somebody tell me what's going on! (don't wanne read all the 20 pages!)

[thaibebop]

Echo?

[kayo]

Echo

Echo

Wakko

Kayo