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| Cullis C.E. — Matrices and Determinoids |
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| Предметный указатель |
Sum of similar affected 119 123
Sum of similar affected inferior simple minor detoids, long-cut 136 (see also “Simple minor Sum.”)
Sum of similar affected inferior simple minor detoids, short-cut 134
Superior simple minors 116 119 123 140—3
Symmetrical forms of the general solution of any system of linear algebraic equations 399—404
Symmetrical forms of the general solution of any system of linear algebraic equations of a homogeneous system 392—4
Symmetrical matrix (see “Self-conjugate”)
System of homogeneous linear algebraic equations 380 386 392 404
System of homogeneous linear algebraic equations, Condition that all solutions shall be extravagant 409
System of homogeneous linear algebraic equations, definitions, condition for non-zero solutions 381
System of homogeneous linear algebraic equations, definitions, extravagant and non-extravagant solutions, unit solutions, zero solutions 404
System of homogeneous linear algebraic equations, definitions, matrix of the system 380
System of homogeneous linear algebraic equations, definitions, orthogonal solutions 405
System of homogeneous linear algebraic equations, examples of 390—1
System of homogeneous linear algebraic equations, extravagant solutions; are self-orthogonal 405
System of homogeneous linear algebraic equations, general solution, ordinary forms 381—2
System of homogeneous linear algebraic equations, general solution, symmetrical form 392—3
System of n unconnected equations in n variables 376—7
System of unconnected equations 371
Systems in which all solutions are extravagant or all solutions are mutually orthogonal 391 392 409—10
Systems of linear algebraic equations in general 365 373 395 399—411
Systems of linear algebraic equations in general, Complete sets of mutually orthogonal real solutions of a real system 411
Systems of linear algebraic equations in general, General solution, Ordinary forms 368—9 375-6
Systems of linear algebraic equations in general, Infinite solutions 403—4
Systems of linear algebraic equations in general, Mutually orthogonal solutions 411—12
Systems of linear algebraic equations in general, Symmetrical forms 400—3
Systems of real equations 387 389 406
The inverse and reciprocal of a non-singular matrix are undegenerate 267
Total affects vi 24
Unaffected elements vi.
Unaffected elements, derived products 24
| Unaffected elements, detants 249 252—60
Unaugmented matrices of the matrix equations AX=C, XB=C, AXB=C 312 327 337
Unaugmented solutions of systems of linear algebraic equations 395 397 402 411
Unconnected connections between the rows of a matrix 326 337
Unconnected linear equations 365 371 376 383 415
Unconnected linear equations, linear functions 365
Unconnected linear equations, rows of a functional matrix 295
Unconnected linear equations, rows of a matrix 269
Unconnected solutions 395
Unconnected solutions of systems of linear equations 386 395
Unconnected solutions, Determination of all possible complete sets of 388 397 399
Undegenerate matrix, complete matrices of its minor detants are undegenerate 289
Undegenerate matrix, defined 265
Undegenerate matrix, if the product of two matrices is a non-zero scalar matrix (or an undegenerate square matrix), the factor matrices are undegenerate 267
Undegenerate square matrix has a unique undegenerate inverse 183 267 309
Undegenerate square matrix, beciprocal and conjugate reciprocal are undegenerate 267 289
Unit matrix, defined, notation for 11 177
Unit matrix, occurring as factor in a matrix product 177 207 219 231
Unreduced order of a simple minor 116
Vertical affects vi 24 87
Vertical affects, minors 233 249
Vertical affects, moves 48
Vertical affects, steps 4
Vertical affects, suffixes 6 12
Zero matrix 155 207
Zero rank 265
Zeros, rows of active, in a matrix product 200—1
Zeros, rows of final, in any matrix 154
Zeros, rows of long, in a detoid 107
Zeros, rows of passive, in a matrix product 196—8
Zeros, rows of short, in a detoid 112
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