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403.1999969 0 0 336.9600067 0 239.0399933 cm
/Im0 Do
Q
q
403.1999969 0 0 239.0399933 0 0 cm
/Im1 Do
Q
BT
/T1_0 1 Tf
0.0136 Tc 3 Tr 9.1 0 0 9.1 39.92 549.91 Tm
(Proof: )Tj
0.0323 Tc 3.064 0 Td
(In )Tj
0.0407 Tc 1.251 0 Td
(this )Tj
0.0125 Tc 2.01 0 Td
(case, )Tj
/T1_1 1 Tf
0 Tc 9.4 0 0 9.4 120.14 549.91 Tm
(H )Tj
/T1_0 1 Tf
0.0164 Tc 9.1 0 0 9.1 131.45 549.91 Tm
(satisfies )Tj
0.05 Tc 9.5625 0 0 9.1 165.94 549.91 Tm
(the )Tj
0.0401 Tc 9.1 0 0 9.1 182.43 549.91 Tm
(condition )Tj
0.0182 Tc 4.49 0 Td
(of )Tj
0.05 Tc 9.1244 0 0 9.1 234.16 549.91 Tm
(theorem )Tj
9.4049 0 0 9.1 269.96 549.91 Tm
(4, )Tj
0.0425 Tc 9.1 0 0 9.1 281.33 549.91 Tm
(with )Tj
0 Tc 8.7 0 0 8.7 302.2 549.91 Tm
(m )Tj
13 0 0 13 313.31 549.91 Tm
(= )Tj
/T1_1 1 Tf
0.0137 Tc 9.4 0 0 9.4 323.06 549.91 Tm
(2k. )Tj
/T1_0 1 Tf
0 Tc 7.6 0 0 7.6 362.62 549.91 Tm
(0 )Tj
-0.0325 Tc 9.1 0 0 9.1 40 526.69 Tm
(Now )Tj
-0.035 Tc 8.9557 0 0 9.1 62.27 526.69 Tm
(we )Tj
0.0294 Tc 9.1 0 0 9.1 77.32 526.69 Tm
(generalize )Tj
0.05 Tc 9.6991 0 0 9.1 121.66 526.69 Tm
(the )Tj
9.2757 0 0 9.1 139.48 526.69 Tm
(theorem )Tj
0.0379 Tc 9.1 0 0 9.1 177.21 526.69 Tm
(of )Tj
0.05 Tc 9.1254 0 0 9.1 189.68 526.69 Tm
(Brualdi )Tj
9.3999 0 0 9.1 224.54 526.69 Tm
(and )Tj
9.3336 0 0 9.1 244.3 526.69 Tm
(Newman )Tj
9.1016 0 0 9.1 284.69 526.69 Tm
(in )Tj
9.3153 0 0 9.1 296.91 526.69 Tm
(another )Tj
9.1677 0 0 9.1 332.73 526.69 Tm
(direction. )Tj
0 Tc 9.1 0 0 9.1 25.54 515.17 Tm
(A )Tj
0.03 Tc 1.238 0 Td
(complex )Tj
0.05 Tc 9.5284 0 0 9.1 73.42 515.17 Tm
(matrix )Tj
/T1_1 1 Tf
0 Tc 9.1 0 0 9.1 105.08 515.17 Tm
(A )Tj
/T1_0 1 Tf
-0.0169 Tc 1.104 0 Td
(is )Tj
0.0298 Tc 1.165 0 Td
(called )Tj
/T1_1 1 Tf
0.0436 Tc 3.02 0 Td
(skew-Hermitian )Tj
/T1_0 1 Tf
0.0391 Tc 7.407 0 Td
(if )Tj
/T1_1 1 Tf
-0.035 Tc 8.914 0 0 9.1 230.36 515.17 Tm
(A* )Tj
0.05 Tc 12.8471 0 0 10.1 256.04 515.17 Tm
(-A, )Tj
/T1_0 1 Tf
0.0288 Tc 9.1 0 0 9.1 277.37 515.17 Tm
(where )Tj
/T1_2 1 Tf
0 Tc 13.1 0 0 13.1 304.98 515.17 Tm
(* )Tj
/T1_0 1 Tf
0.05 Tc 9.2007 0 0 9.1 313.37 515.17 Tm
(represents )Tj
9.5625 0 0 9.1 359.44 515.17 Tm
(the )Tj
9.2478 0 0 9.1 25.52 503.6499 Tm
(Hermitian )Tj
0.0387 Tc 9.1 0 0 9.1 69.93 503.6499 Tm
(adjoint. )Tj
0.05 Tc 10.5977 0 0 9.1 25.47 482.05 Tm
(Theorem )Tj
0 Tc 9.3 0 0 9.3 71.18 482.05 Tm
(7 )Tj
/T1_1 1 Tf
0.009 Tc 9.1 0 0 9.1 82.25 482.05 Tm
(There )Tj
0.0037 Tc 2.738 0 Td
(is )Tj
0.0448 Tc 0.976 0 Td
(no )Tj
0.05 Tc 9.1168 0 0 9.1 128.78 482.05 Tm
(Hermitian )Tj
0.0357 Tc 9.1 0 0 9.1 173.52 482.05 Tm
(\(or )Tj
0.0407 Tc 1.605 0 Td
(skew-Hermitian\) )Tj
0.0331 Tc 7.684 0 Td
(circulant )Tj
0.0212 Tc 4.253 0 Td
(complex )Tj
0.05 Tc 9.1582 0 0 9.1 330.74 482.05 Tm
(Hadamard )Tj
9.3149 0 0 9.1 25.88 470.53 Tm
(matrix )Tj
10.0385 0 0 9.1 56.08 470.53 Tm
(of )Tj
0.0185 Tc 9.1 0 0 9.1 67.25 470.53 Tm
(order )Tj
0 Tc 2.574 0 Td
(n )Tj
/T1_0 1 Tf
10.1 0 0 10.1 99.85 470.53 Tm
(> )Tj
-0.0226 Tc 9.1 0 0 9.1 109.04 470.53 Tm
(4. )Tj
0.0136 Tc -7.576 -2.393 Td
(Proof: )Tj
0.0345 Tc 3.052 0 Td
(Suppose )Tj
0 Tc 4.004 0 Td
(a )Tj
0.05 Tc 9.2883 0 0 9.1 111.92 448.75 Tm
(Hermitian )Tj
9.1094 0 0 9.1 156.51 448.75 Tm
(circulant )Tj
0.0333 Tc 9.1 0 0 9.1 195.75 448.75 Tm
(complex )Tj
0.05 Tc 9.5604 0 0 9.1 232.16 448.75 Tm
(Hadamard )Tj
9.1355 0 0 9.1 278.8 448.75 Tm
(matrix, )Tj
/T1_1 1 Tf
0 Tc 9.8 0 0 9.8 311.73 448.75 Tm
(A )Tj
/T1_2 1 Tf
13.6 0 0 13.6 320.54 448.75 Tm
(+ )Tj
/T1_1 1 Tf
0.05 Tc 10.3264 0 0 9.8 330.02 448.75 Tm
(Bi, )Tj
/T1_0 1 Tf
0.044 Tc 9.1 0 0 9.1 346.58 448.75 Tm
(exists. )Tj
0.05 Tc 9.467 0 0 9.1 25.66 437.05 Tm
(Then )Tj
/T1_1 1 Tf
0 Tc 9.8 0 0 9.8 51.63 437.05 Tm
(A )Tj
/T1_0 1 Tf
0.05 Tc 9.3999 0 0 9.1 62.54 437.05 Tm
(and )Tj
/T1_1 1 Tf
0 Tc 9.8 0 0 9.8 82.33 437.05 Tm
(B )Tj
/T1_0 1 Tf
0.0488 Tc 9.1 0 0 9.1 93.87 437.05 Tm
(are )Tj
0.0457 Tc 1.859 0 Td
(circulant, )Tj
/T1_1 1 Tf
0 Tc 9.8 0 0 9.8 153.87 437.05 Tm
(A )Tj
/T1_0 1 Tf
12.4 0 0 12.4 165.9 437.05 Tm
(= )Tj
/T1_1 1 Tf
0.0361 Tc 9.8 0 0 9.8 178.17 437.05 Tm
(At )Tj
/T1_0 1 Tf
0.05 Tc 9.2824 0 0 9.1 192.33 437.05 Tm
(and )Tj
/T1_1 1 Tf
0 Tc 9.8 0 0 9.8 211.93 437.05 Tm
(B )Tj
/T1_0 1 Tf
12.4 0 0 12.4 224.4 437.05 Tm
(= )Tj
/T1_1 1 Tf
0.05 Tc 11.6854 0 0 9.8 236.61 437.05 Tm
(-Bt. )Tj
/T1_0 1 Tf
0.0467 Tc 9.1 0 0 9.1 264.43 437.05 Tm
(So )Tj
/T1_1 1 Tf
0.0368 Tc 9.8 0 0 9.8 279.52 437.05 Tm
(\(A )Tj
/T1_2 1 Tf
0 Tc 12.9 0 0 12.9 292.83 437.05 Tm
(+ )Tj
/T1_1 1 Tf
0.05 Tc 10.4332 0 0 9.8 303.2 437.05 Tm
(Bi\)\(A )Tj
/T1_2 1 Tf
0 Tc 13.6 0 0 13.6 331.34 437.05 Tm
(+ )Tj
/T1_1 1 Tf
0.05 Tc 13.949 0 0 9.8 342.1 437.05 Tm
(Bit )Tj
0 Tc 12.1 0 0 12.1 365.59 437.05 Tm
(= )Tj
9.8 0 0 9.8 25.89 425.89 Tm
(A )Tj
/T1_0 1 Tf
5.7 0 0 5.7 32.91 429.31 Tm
(2 )Tj
/T1_2 1 Tf
11.7 0 0 11.7 39.77 425.89 Tm
(+ )Tj
/T1_1 1 Tf
0.05 Tc 10.1271 0 0 9.8 49.46 425.89 Tm
(2ABi )Tj
-0.035 Tc 9.3715 0 0 9.8 85.21 425.89 Tm
(B2 )Tj
/T1_2 1 Tf
0 Tc 8.1 0 0 8.1 101.03 425.89 Tm
(= )Tj
/T1_1 1 Tf
0.05 Tc 10.6453 0 0 9.7 112.26 425.89 Tm
(nI. )Tj
/T1_2 1 Tf
10.8168 0 0 8.7 133.08 425.89 Tm
(It )Tj
/T1_0 1 Tf
-0.0018 Tc 9.1 0 0 9.1 144.08 425.89 Tm
(follows )Tj
0.05 Tc 9.9596 0 0 9.1 176.38 425.89 Tm
(that )Tj
/T1_1 1 Tf
10.9545 0 0 9.8 198.35 425.89 Tm
(AB )Tj
/T1_2 1 Tf
0 Tc 8.1 0 0 8.1 217.31 425.89 Tm
(= )Tj
/T1_0 1 Tf
9.1 0 0 9.1 229.05 425.89 Tm
(0 )Tj
0.05 Tc 9.2824 0 0 9.1 237.87 425.89 Tm
(and )Tj
/T1_1 1 Tf
-0.035 Tc 8.914 0 0 9.8 257.18 425.89 Tm
(A2 )Tj
/T1_0 1 Tf
0 Tc 9.8 0 0 9.8 271.51 425.89 Tm
(-)Tj
/T1_1 1 Tf
-0.035 Tc 9.2041 0 0 9.8 281.95 425.89 Tm
(B2 )Tj
/T1_2 1 Tf
0 Tc 8.1 0 0 8.1 297.41 425.89 Tm
(= )Tj
/T1_1 1 Tf
0.05 Tc 10.491 0 0 9.7 308.83 425.89 Tm
(nI. )Tj
/T1_0 1 Tf
9.1528 0 0 9.1 329.86 425.89 Tm
(Therefore, )Tj
/T1_1 1 Tf
0 Tc 9.7 0 0 9.7 25.82 414.3699 Tm
(H )Tj
/T1_2 1 Tf
8.7 0 0 8.7 37.3 414.3699 Tm
(= )Tj
/T1_1 1 Tf
9.8 0 0 9.8 47.13 414.3699 Tm
(A )Tj
/T1_2 1 Tf
12.9 0 0 12.9 55.41 414.3699 Tm
(+ )Tj
/T1_1 1 Tf
9.8 0 0 9.8 64.33 414.3699 Tm
(B )Tj
/T1_0 1 Tf
-0.035 Tc 8.7827 0 0 9.1 74.27 414.3699 Tm
(is )Tj
0 Tc 9.1 0 0 9.1 83.43 414.3699 Tm
(a )Tj
0.0456 Tc 0.791 0 Td
(circulant )Tj
0.05 Tc 9.4404 0 0 9.1 129.2 414.3699 Tm
(Hadamard )Tj
9.4781 0 0 9.1 174.76 414.3699 Tm
(matrix, )Tj
9.1649 0 0 9.1 208.17 414.3699 Tm
(and )Tj
/T1_1 1 Tf
-0.035 Tc 8.8446 0 0 9.7 226.15 414.3699 Tm
(H2 )Tj
/T1_0 1 Tf
8.7827 0 0 9.1 240.59 414.3699 Tm
(is )Tj
0.05 Tc 9.2011 0 0 9.1 249.71 414.3699 Tm
(symmetric. )Tj
9.349 0 0 9.1 299.26 414.3699 Tm
(The )Tj
9.1871 0 0 9.1 318.05 414.3699 Tm
(result )Tj
0.0114 Tc 9.1 0 0 9.1 344.06 414.3699 Tm
(follows )Tj
0.0382 Tc -35.031 -1.266 Td
(from )Tj
0.029 Tc 2.474 0 Td
(corollary )Tj
-0.035 Tc 8.343 0 0 8.7 86.12 402.85 Tm
(6. )Tj
0.05 Tc 9.349 0 0 9.1 97.66 402.85 Tm
(The )Tj
0.047 Tc 9.1 0 0 9.1 116.69 402.85 Tm
(skew-Hermitian )Tj
0.0274 Tc 7.402 0 Td
(case )Tj
-0.0084 Tc 2.135 0 Td
(follows )Tj
0.0316 Tc 3.343 0 Td
(from )Tj
0.05 Tc 9.4259 0 0 9.1 256.12 402.85 Tm
(the )Tj
0.0363 Tc 9.1 0 0 9.1 272.79 402.85 Tm
(observation )Tj
0.05 Tc 10.0691 0 0 9.1 322.18 402.85 Tm
(that )Tj
/T1_3 1 Tf
0 Tc 9 0 0 9 343.32 402.85 Tm
(A )Tj
/T1_2 1 Tf
12.9 0 0 12.9 352.77 402.85 Tm
(+ )Tj
/T1_1 1 Tf
0.05 Tc 10.7508 0 0 9.8 362.42 402.85 Tm
(Bi )Tj
/T1_0 1 Tf
-0.0169 Tc 9.1 0 0 9.1 25.49 391.5099 Tm
(is )Tj
0.05 Tc 9.1667 0 0 9.1 35.6 391.5099 Tm
(Hermitian )Tj
0.0193 Tc 9.1 0 0 9.1 79.31 391.5099 Tm
(if )Tj
0.05 Tc 9.2824 0 0 9.1 87.93 391.5099 Tm
(and )Tj
0.0342 Tc 9.1 0 0 9.1 105.93 391.5099 Tm
(only )Tj
0.0391 Tc 2.257 0 Td
(if )Tj
/T1_3 1 Tf
0 Tc 9 0 0 9 135.61 391.5099 Tm
(B )Tj
/T1_2 1 Tf
1.103 0 Td
(-)Tj
/T1_1 1 Tf
0.05 Tc 10.2335 0 0 9.8 154.77 391.5099 Tm
(Ai )Tj
/T1_0 1 Tf
-0.0169 Tc 9.1 0 0 9.1 167.87 391.5099 Tm
(is )Tj
0.0399 Tc 1.062 0 Td
(skew-Hermitian. )Tj
/T1_2 1 Tf
0 Tc 6.9001 0 0 6.9001 363.16 391.5099 Tm
(0 )Tj
/T1_0 1 Tf
0.05 Tc 10.4322 0 0 9.1 40.27 368.2899 Tm
(Remark. )Tj
0.0125 Tc 9.1 0 0 9.1 84 368.2899 Tm
(In )Tj
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([4] )Tj
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(\(1984\), )Tj
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(dI )Tj
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(\)"J, )Tj
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[(Lin. )-262(Alg. )]TJ
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([5] )Tj
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(a )Tj
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(Brualdi )Tj
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(Newman, )Tj
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(Lin. )Tj
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(\(1987\), )Tj
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(pp. )Tj
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(39-43. )Tj
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([6] )Tj
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(H. )Tj
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(J. )Tj
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(RYSER, )Tj
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(Mathematics, )Tj
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(Monographs, )Tj
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(MAAj )Tj
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(Wiley )Tj
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(1963. )Tj
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([7] )Tj
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(R. )Tj
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(TURYN, )Tj
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(15 )Tj
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(\(1965\), )Tj
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(pp. )Tj
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(319-346. )Tj
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([8] )Tj
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(--, )Tj
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(Complex )Tj
0.0345 Tc 4.123 0 Td
(Hadamard )Tj
0.0354 Tc 4.971 0 Td
(matrices, )Tj
/T1_0 1 Tf
0.05 Tc 9.3236 0 0 9.1 189.1 97.75 Tm
(in )Tj
0.0484 Tc 9.1 0 0 9.1 200.61 97.75 Tm
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(Structures )Tj
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(and )Tj
9.41 0 0 9.1 325.42 97.75 Tm
(their )Tj
0.0372 Tc 9.1 0 0 9.1 348.46 97.75 Tm
(Appli\255)Tj
0.0349 Tc -33.693 -1.247 Td
(cations, )Tj
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(New )Tj
0.0091 Tc 2.288 0 Td
(York, )Tj
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(1970, )Tj
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(pp. )Tj
0.0128 Tc 9.4 0 0 9.4 162.68 86.3999 Tm
(435-437. )Tj
/T1_1 1 Tf
0.05 Tc 9.7309 0 0 7.9001 161.27 63.55 Tm
(\(Received )Tj
9.8132 0 0 7.9001 209.07 63.55 Tm
(4/11/92\) )Tj
/T1_2 1 Tf
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(227 )Tj
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