Other Index 6: Higher geometry of fields and matrix theory

1. █ Divider: 6
2. █ Section Title: Higher geometry of fields and matrix theory
3. █ Equation of the plane which contains n consecutive points of the path, 1829.
4. █ A path is fixed (in a given field) by any n combinations of t and x, 1425.
5. █ If some variables in a complete system are unobservable, a path fixed by n t,x combinations can be accertained empirically, by using substitute variables, 1413, numerical example 1470.
6. █ Knowledge of one form EXPRESSION for all values of xº₁...xº_n;t is sufficient to define all the others. 5051.
7. █ Field cannot be transformed to show all the variables but one as part-functions 3764.
8. █ Numerical arrangement for maximal stability, 2529.
9. █ If, as matrices, EXPRESSION, then EXPRESSION, 1828.
10. █ Method for finding EXPRESSION [Lim x_i, t?8], 2179.
11. █ Matrix representation with zero in main diagonal as premultiplier 2395.
12. █ Lists of numerical matrices suitable for sampling experiments: 5x5 { 2335 2336 2337 2338 2339 2340 2341 2342 2343 2344 2345 2346 2347 2348 2349 } , { 2402 2403 2404 2405 2406 2407 2408 2409 } , 4x4 { 2350 2351 2352 2353 2354 2355 2356 2357 2358 2359 } , { 2380 2381 2382 2383 2384 2385 2386 2387 2388 2389 } , 3x3 { 2368 2369 2370 2371 2372 2373 2374 2375 2376 2377 2378 } , 2x2 { 2362 2363 2364 2365 2366 }
13. █ M=MATRIX If latent roots of M equal none of those of A, neither B nor C can be wholly zero, 2655.
14. █ Determinant and latent roots of a matrix formed by adding a diagonal and a 'permutation' matrix, 3429, applied 3433.
15. █ If EQUATION, with roots r₁,...,r_n, to find ?r_p/?a_St, 0750, 1824. i.e. effect of coefficient on a root. Example 2066, 2401.
16. █ The latent roots are invariant when variables are replaced by derivatives. 3717, 3719.
17. █ An electromechanical analogy (spring and mass / condenser etc) in detail 4998.
18. █ Test for stability by dominant root, 2072.
19. █ Finding latent roots by Mallock machine, 2179.
20. █ Forming system with given roots 1818, 2444.
21. █ Test for stability of EQUATION [x'=Ax] by complex variable theory, 2030. An example 2267.
22. █ If one variable is made more self-stable, the whole may become unstable, 2423, 2454, 2463, 2458, 2460.
23. █ If a number, positive or negative, is added to all non-diagonal elements, the system becomes unstable when the number is large enough, 2772.
24. █ Characteristic equation of MATRIX 2780.
25. █ If A dominates B, the latent roots of the whole are just those of A and those of B, 2678.
26. █ If a_jk=a_jk + ib_jk, and [a_jk] has roots ?₁...?_n, then MATRIX has roots ?₁...?_n , ?₁* ... ?_n* 3917.
27. █ Nearly-decomposible matrices. Reprint 125.
28. █ Transforming a matrix to reduced form 5297.
29. █ Graphs and asymptotic forms of finite Boolean relation matrices and stochastic matrices. Reprint 193.
30. █ (Mod 12) MATRIX has VECTOR as equilibrium (and 23 other, given, vectors), 6163.