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Eigengap

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133: 174: 167: 193: 160: 198: 77: 105: 59: 55: 68:; although the spectral gap may often be defined in a broader sense than that of the eigengap. 113: 96:
Davis, C.; W. M. Kahan (March 1970). "The rotation of eigenvectors by a perturbation. III".
36: 109: 144: 140: 47: 28: 187: 51: 64: 17: 132: 40: 54:, uses the eigengap to show how eigenspaces of an operator change under 117: 148: 43:, where eigenvalues are sorted in ascending order. 168: 8: 62:, the eigengap is often referred to as the 46:The Davis–Kahan theorem, named after 175: 161: 39:is the difference between two successive 88: 7: 129: 127: 25: 131: 1: 147:. You can help Knowledge by 215: 126: 78:Eigenvalue perturbation 143:-related article is a 194:Linear algebra stubs 110:1970SJNA....7....1D 98:SIAM J. Numer. Anal 60:spectral clustering 18:Davis-Kahan theorem 156: 155: 16:(Redirected from 206: 177: 170: 163: 135: 128: 122: 121: 93: 21: 214: 213: 209: 208: 207: 205: 204: 203: 184: 183: 182: 181: 125: 118:10.1137/0707001 95: 94: 90: 86: 74: 37:linear operator 23: 22: 15: 12: 11: 5: 212: 210: 202: 201: 199:Linear algebra 196: 186: 185: 180: 179: 172: 165: 157: 154: 153: 141:linear algebra 136: 124: 123: 87: 85: 82: 81: 80: 73: 70: 48:Chandler Davis 29:linear algebra 24: 14: 13: 10: 9: 6: 4: 3: 2: 211: 200: 197: 195: 192: 191: 189: 178: 173: 171: 166: 164: 159: 158: 152: 150: 146: 142: 137: 134: 130: 119: 115: 111: 107: 103: 99: 92: 89: 83: 79: 76: 75: 71: 69: 67: 66: 61: 57: 53: 52:William Kahan 49: 44: 42: 38: 34: 30: 19: 149:expanding it 138: 101: 97: 91: 65:spectral gap 63: 56:perturbation 45: 32: 26: 104:(1): 1–46. 41:eigenvalues 188:Categories 84:References 72:See also 33:eigengap 106:Bibcode 31:, the 139:This 58:. In 35:of a 145:stub 50:and 114:doi 27:In 190:: 112:. 100:. 176:e 169:t 162:v 151:. 120:. 116:: 108:: 102:7 20:)

Index

Davis-Kahan theorem
linear algebra
linear operator
eigenvalues
Chandler Davis
William Kahan
perturbation
spectral clustering
spectral gap
Eigenvalue perturbation
Bibcode
1970SJNA....7....1D
doi
10.1137/0707001
Stub icon
linear algebra
stub
expanding it
v
t
e
Categories
Linear algebra stubs
Linear algebra

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