Fuhrmann P.A. — A Polynomial Approach to Linear Algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Fuhrmann P.A. — A Polynomial Approach to Linear Algebra

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Название: A Polynomial Approach to Linear Algebra

Автор: Fuhrmann P.A.

Аннотация:

Text heavily biased toward functional methods. Discusses the Hankel norm approximation for the case of scalar rational functions. Paper. DLC: Algebras, Linear.

Язык:

Рубрика: Математика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1996

Количество страниц: 393

Добавлена в каталог: 10.03.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abelian group      3
Adjoint transformation      84 157
All-pass function      314
Annihilator      79
atoms      229
Backward invariant subspace      312
Backward shift operator      111
Balanced realization      350
Barnett factorization      204
Basis      37
Basis transformation matrix      47
Bessel inequality      153
Beurling’s theorem      315
Bezout equation      10
Bezout form      200
Bezout identity      10
Bezoutian      200
Bilinear form      188
Binary operation      3
Binary relation      1
Canonical embedding      82
Canonical factorization      2
Canonical projection      7
Canonical system      277
Cauchy determinant      63
Cauchy index      240
Causality      275
Cayley transform      168
Characteristic polynomial      92
Characteristic value      92
Characteristic vector      92
Chinese remainder theorem      113
Christoffel — Darboux formula      302
Circulant matrix      107
Classical adjoint      58
Codimension      43
Cofactor      54
Commutant      128
Companion matrices      99
composition      2
Congruence      189
Continued fraction representation      229
Control basis      98
Controllability realization      288
Controller realization      288
Coordinate vector      45
coordinates      45
Coprime factorization      22
Coprimeness      10 314
Coset      4
Cramer’s Rule      58
Cyclic transformation      127
Cyclic vector      127
Degree      11
Determinant      53
Determinant rank      95
Determinantal divisors      136
Diagonalizable operator      141 145
DIMENSION      39
Direct sum      41
Divisor      10
DSS factorization      319
Dual basis      79
Dual Jordan basis      132
Dual space      77
Eigenvalue      92
Eigenvector      92
Entire ring      21
Equivalence classes      4
Equivalence of polynomial matrices      135
Equivalence relation      1
Euclidean algorithm      14
Euclidean ring      12
Exact sequence      29
External representation      272
Factor      10
Factor group      6
Field      8
Field of quotients      22
Final space      175
Formal power series      20
Fractional linear transformation      230
Free module      32
Function      1
Functional equation of Hankel operators      197
Fundamental polynomial equation      326
Generalized Christoffel-D arboux formula      232
Generalized Euclidean algorithm      249
Generating function      200 253
Generator      10
Gohberg — Semencul formula      206
Gram matrix      172
Gram — Schmidt orthonormalization      154
Gramian      172 350
Greatest common divisor      10 16
Group      3
Hankel functional equation      319
Hankel operator      196 310 319
Hautus test      300
Hermite interpolation      114
Hermite — Fujiwara quadratic form      256
Hermite — Hurwitz theorem      241
Hermitian adjoint      157
Hermitian form      152 189
Hermitian operator      164
Homomorphism      5
Hurwitz determinants      262
Hurwitz polynomial      255
Hyperspace      81
Ideal      9
Image      66
INDEX      5
Induced map      7 89
Initial space      175
Injective map      2
Inner function      314
Inner product      151
Input space      273
Input/output relations      272
Integral domain      21
Internal representation      272
Internal stability      298
Interpolation basis      98
Intertwining map      87
Invariant factor algorithm      135
Invariant factors      136
Invariant subspace      87 312
Invertible transformation      70
Involuted Hankel operator      310
Irreducible polynomial      17
Isometric isomorphism      160
Isometry      160
Isomorphic factorizations      281
Isomorphism      6
Jacobi signature rule      245
Jacobson chain matrix      124

Jordan Basis      131
Kernel      66
Kronecker’s theorem      198 321
Lagrange interpolation      48
Lagrange reduction method      190
Lanczos polynomials      230
Laurent operator      116 310
Least common multiple      16
Left inverse      8
Left invertible transformation      70
Levinson algorithm      248
linear combination      35
Linear functional      77
Linear independence      37
Linear space      33
Linear transformation      65
MAP      1
Markov parameters      277
Matrix representation      74
McMillan degree      198
Minimal polynomial      93
Minimal rational extension      222
Minimax principle      167
Minimum phase function      24
Minor      54
Module      29
Moebius transformation      230
Monic polynomial      17
Multiplicative set      21
Mutual coprimeness      42
Nehari’s theorem      337
Nevanlinna — Pick interpolant      337
Newton sums      252
Norm      152
Normal operator      169
Normal subgroup      5
Nullity      67
Observability      279
Observability map      277
Observability realization      288
Observer      294
Observer realization      289
Operator norm      157
Order      5
Orlando’s formula      268
Orthogonal basis      154 237
Orthogonality      152
Orthonormal basis      154
Orthonormal set      152
Output space      273
Parallelogram identity      153
Partial isometry      175
Partition      1
Polar decomposition      174
Polarization identity      153
Polynomial      10
Polynomial model      97
Positive operator      172
Positive pair      256
Positive sequence      246
Primary decomposition      18
Prime polynomial      17
Principal ideal      10
Principal ideal domain      10
PRODUCT      2
Proper rational functions      23
Quadratic form      189
Quotient module      30
Quotient ring      9
Rank      67 194
Rational control basis      215
Rational functions      22 110
Rational model      112
Reachability      279
Reachability map      277
Real Jordan form      134
Real pair      256
Reducible polynomial      17
Reducing subspace      87
Relative degree      23
Reproducing kernel      122
Restricted input/output map      276
Restriction of a map      89
Reverse polynomial      204
Right inverse      8
Right invertible transformation      70
Ring      8
Ring embedding      21
Ring homomorphism      8
Ring of quotients      21
Schmidt pair      178
Schur parameters      247
Schwarz inequality      152
Self-adjoint operator      164
Sesquilinear form      188
Shift operator      97
Shift realization      285
Short exact sequence      29
Signature      194
Similarity      87
Singular value      178
Singular vectors      178
Spanning set      37
Spectral basis      98
Stable polynomial      255
Stable rational functions      24
Standard basis      48 98
State space      273
State space isomorphism      282
State space realization      273
Strict causality      275
Subgroup      4
Submodule      29
subspace      35
Sum of squares      193
Surjective map      2
Sylvester resultant      60 206
Sylvester’s law of inertia      190
Sylvester’s resultant      60
Symbol of Hankel operator      196
Symmetric group      55
System singular values      350
Taylor expansion      51
Toeplitz form      246
Toeplitz operator      310
Transfer function      274 275
Triangle inequality      152
Truncated Laurent series      28
Unimodular matrix      135
Unitary equivalence      162
Unitary isomorphism      160
Vandermonde matrix      50
Vector      33
Youla — Kucera parametrization      299
Zero divisor      21
Zero of polynomial      13

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