-
Notifications
You must be signed in to change notification settings - Fork 2
/
references.bib
458 lines (345 loc) · 11.5 KB
/
references.bib
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
%%% =========================================================================
%%% BibTeX-file{
%%% author = "James Quinlan",
%%% affiliation = "University of",
%%% version = "1.01",
%%% date = "28 Sept 2021",
%%% filename = "references.bib",
%%% address = "" ,
%%% telephone = "",
%%% email = "",
%%% checksum = "md5:ec8bcab9c0dff4ad5d072612743e3e72",
%%% keywords = "introduction to matrix theory and linear algebra",
%%% supported = "no",
%%% docstring = "BibTeX bibliography for the article"
%%% }
%%% URL = "https://www.github.com/jamesquinlan/MAT220-Linear-Algebra/"
%%% ==========================================================================
% ---------- A ------------ %
% Abad
@InProceedings{abad_2009,
author="Abad, Manuel F.
and Gass{\'o}, Mar{\'i}a T.
and Torregrosa, Juan R.",
editor="Bru, Rafael
and Romero-Viv{\'o}, Sergio",
title="Inverse-Positive Matrices with Checkerboard Pattern",
booktitle="Positive Systems",
year="2009",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="185--194",
abstract="A nonsingular real matrix A is said to be inverse-positive if all the elements of its inverse are nonnegative. This class of matrices contains the M-matrices, from which inherit some of their properties and applications, especially in Economy. In this work we analyze the inverse-positive concept for a particular type of pattern: the checkerboard pattern. In addition, we study the Hadamard product of certain classes of inverse-positive matrices whose entries have a particular sign pattern.",
isbn="978-3-642-02894-6"
}
% Abu-Jeib
@article{abu2004rank,
title={Rank-One Perturbations and Transformations of Centrosymmetric M atrices},
author={Abu-Jeib, I},
journal={New Zealand J. Math},
volume={33},
number={1},
pages={1--10},
year={2004},
annote={},
keywords={Centrosymmetric, Rank-One Perturbations}
}
% Abu-Jeib
@article{abu2005counteridentity,
title={On the counteridentity matrix},
author={Abu-Jeib, Iyad T},
journal={Missouri J. Math. Sci},
volume={17},
number={1},
pages={26--34},
year={2005},
annote={A simple approach to deriving results/algorithms about centrosymmetric matrices.
Also, we reveal new facts about centrosymmetric and skew-centrosymmetric matrices, and we present a new characterization of centrosymmetric matrices and skew-centrosymmetric matrices.},
keywords={Centrosymmetric, counteridentity}
}
% Abu-Jeib
@article{abu2002c,
title={Centrosymmetric Matrices: Properties and an Alternative Approach},
author={Abu-Jeib, IYAD T},
journal={Canadian Applied Mathematics Quarterly},
volume={10},
number={4},
pages={429--445},
year={2002},
annote={Presents (i) a new approach to deriving results about centrosymmetric matrices, (ii) new facts about centro-and skew-centrosymmtric matrices, and (iii) new characterization of centro/skew-centrosymmetric matrices.},
keywords={centrosymmetric}
}
% Alan Andrew: Eigenvectors of Certain Matrices
@article{andrew1973eigenvectors,
title={Eigenvectors of certain matrices},
author={Andrew, Alan L},
journal={Linear Algebra and its Applications},
volume={7},
number={2},
pages={151--162},
year={1973},
publisher={Elsevier},
keywords={centrosymmetric}
}
% ----------------- B ------------------- %
@article{bai2004inverse,
title={Inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation},
author={Bai, Zheng-Jian and Chan, Raymond H},
journal={Theoretical Computer Science},
volume={315},
number={2-3},
pages={309--318},
year={2004},
publisher={Elsevier},
apa={Bai, Z. J., \& Chan, R. H. (2004). Inverse eigenproblem for centrosymmetric and centroskew matrices and their approximation. Theoretical Computer Science, 315(2-3), 309-318.},
annote={},
keywords={Centrosymmetric}
}
@book{boyd2018introduction,
title={Introduction to applied linear algebra: vectors, matrices, and least squares},
author={Boyd, Stephen and Vandenberghe, Lieven},
year={2018},
publisher={Cambridge university press}
}
% ----------------- C ------------------- %
% Cantoni
@article{cantoni1976eigenvalues,
title={Eigenvalues and eigenvectors of symmetric centrosymmetric matrices},
author={Cantoni, A and Butler, P},
journal={Linear Algebra and its Applications},
volume={13},
number={3},
pages={275--288},
year={1976},
publisher={Elsevier},
annote={},
keywords={eigenvalues, eigenvectors, centrosymmetric}
}
% Collar, A.R.
@article{collar1962centrosymmetric,
title={On centrosymmetric and centroskew matrices},
author={Collar, AR},
journal={The Quarterly Journal of Mechanics and Applied Mathematics},
volume={15},
number={3},
pages={265--281},
year={1962},
publisher={Oxford University Press},
annote={Some properties of centrosymmetric matrices are described and discussed: in particular, methods are given for determining eigensolutions (latent roots and vectors) of centrosymmetric matrices from those of combinations of submatrices. Similar discussions are given for a class of matrix which may be described as centro-skew. Canonical forms for both centrosymmetric and centroskew matrices are given, and some applications are mentioned.},
keywords={centrosymmetric, centroskew, eigenvalues, applications}
}
% ---------- D ------------ %
% Ding
@article{ding2014matrix,
title={When a matrix and its inverse are nonnegative},
author={Ding, J and Rhee, NH and others},
journal={Missouri Journal of Mathematical Sciences},
volume={26},
number={1},
pages={98--103},
year={2014},
publisher={Central Missouri State University, Department of Mathematics and Computer Science},
annote={},
keywords={Nonnegative Matrix}
}
% Ding
@article{ding2013maacmj,
title={When a matrix and its inverse are nonnegative},
author={Ding, J and Rhee, NH and others},
journal={The College Mathematics Journal},
volume={44},
number={2},
pages={108--109},
year={2013},
publisher={Mathematical Association of America (MAA)},
annote={},
keywords={Nonnegative Matrix}
}
% ------------ G -------------- %
% GOOD
@article{good1970inverse,
title={The inverse of a centrosymmetric matrix},
author={Good, IJ},
journal={Technometrics},
volume={12},
number={4},
pages={925--928},
year={1970},
publisher={Taylor \& Francis Group},
annote={Finds the inverse of a centrosymmetric matrix},
keywords={centrosymmetric, inverse centrosymmetric},
apa={Good, I. J. (1970). The inverse of a centrosymmetric matrix. \texttt{Technometrics, 12}(4), 925-928.}
}
@article{golub1976ill,
title={Ill-conditioned eigensystems and the computation of the Jordan canonical form},
author={Golub, Gene H and Wilkinson, James Hardy},
journal={SIAM review},
volume={18},
number={4},
pages={578--619},
year={1976},
publisher={SIAM}
}
% Grenander. Toeplitz Forms
@book{grenander1984toeplitz,
title={Toeplitz forms and their applications},
author={Grenander, Ulf and Szeg{\"o}, Gabor},
year={1984},
publisher={Univ of California Press},
keywords={Toeplitz Forms, centrosymmetric}
}
% --------------------- H ------------------------ %
% Horn
@book{horn2012matrix,
title={Matrix analysis},
author={Horn, Roger A and Johnson, Charles R},
year={2012},
publisher={Cambridge university press},
annote={},
keywords={Matrix Analysis, Nonnegative Matrix}
}
% ----------- J ----------- %
% Jennings, Alan - Matrix computation for Engineers and Scientists
@book{jenning1980matrix,
title={Matrix Computation for Engineers and Scientists},
author={Jenning, Alan},
year={1980},
publisher={J. Wiley},
annote={},
keywords={}
}
@article{johnson1977hadamard,
title={A Hadamard product involving $n$-matrices},
author={Johnson, Charles R},
journal={Linear and Multilinear Algebra},
volume={4},
number={4},
pages={261--264},
year={1977},
publisher={Taylor \& Francis}
}
@article{johnson1983sign,
title={Sign patterns of inverse nonnegative matrices},
author={Johnson, Charles R},
journal={Linear algebra and its applications},
volume={55},
pages={69--80},
year={1983},
publisher={Elsevier}
}
@article{johnson1982inverse,
title={Inverse M-matrices},
author={Johnson, Charles R},
journal={Linear Algebra and its Applications},
volume={47},
pages={195--216},
year={1982},
publisher={Elsevier}
}
% ---------- L ------------ %
@book{leon2014linear,
title={Linear algebra with applications},
author={Leon, Steven J and De Pillis, Lisette and De Pillis, Lisette G},
year={2014},
publisher={Pearson}
}
% ---------- M ------------ %
@article{markham1972nonnegative,
title={Nonnegative matrices whose inverses are $M$-matrices},
author={Markham, Thomas L},
journal={Proceedings of the American Mathematical Society},
volume={36},
number={2},
pages={326--330},
year={1972}
}
% Meyer book
@book{meyer2000matrix,
title={Matrix analysis and applied linear algebra},
author={Meyer, Carl D},
volume={71},
year={2000},
publisher={Siam},
annote={Meyer book on linear algebra},
keywords={Meyer book}
}
% ------------ P ----------- %
@article{pena1995m,
title={M-matrices whose inverses are totally positive},
author={Pe{\~n}a, Juan M},
journal={Linear algebra and its applications},
volume={221},
pages={189--193},
year={1995},
publisher={Elsevier}
}
% Abstract: Characterize the class of totally positive matrices whose inverses are M-matrices (improvement of Markham's).
Also, charatertize the set of M-matrices whose inverses are totally positive (formed by tridiagonal M-matrices)
% ------------ R ----------- %
% Ray, Inverse Toeplitz
@article{ray1970inverse,
title={The inverse of a finite Toeplitz matrix},
author={Ray, WD},
journal={Technometrics},
volume={12},
number={1},
pages={153--156},
year={1970},
publisher={Taylor \& Francis Group},
keywords={Toeplitz}
}
@article{reid1997classroom,
title={Classroom Note: Some Eigenvalue Properties of Persymmetric Matrices},
author={Reid, Russell M},
journal={Siam Review},
volume={39},
number={2},
pages={313--316},
year={1997},
publisher={SIAM},
keywords={Persymmetric, Eigenvalues}
}
% ---------- S ------------ %
% Strang
@article{strang1989patterns,
title={Patterns in linear algebra},
author={Strang, Gilbert},
journal={American Mathematical Monthly},
volume={96},
number={2},
pages={105--117},
year={1989},
publisher={Mathematical Association of America},
annote={},
keywords={Nonnegative Matrix}
}
@article{strang2021introduction,
title={Introduction to Linear Algebra},
author={Strang, Gilbert},
year={2021},
publisher={Cambridge University Press}
}
% ---------- W ------------ %
@article{weaver1985centrosymmetric,
title={Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors},
author={Weaver, James R},
journal={The American Mathematical Monthly},
volume={92},
number={10},
pages={711--717},
year={1985},
publisher={Taylor \& Francis},
keywords={Centrosymmetric},
apa={Weaver, J. R. (1985). Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors. \textit{The American Mathematical Monthly}, 92(10), 711-717.}
}
@article{willoughby1977inverse,
title={The inverse M-matrix problem},
author={Willoughby, Ralph A},
journal={Linear algebra and its applications},
volume={18},
number={1},
pages={75--94},
year={1977},
publisher={Elsevier}
}
% /EOF