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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 대수학 일반
· ISBN : 9781138591462
· 쪽수 : 292쪽
· 출판일 : 2018-05-17
목차
- A unified framework
- Common symmetric patterned matrices
- Patterned XX matrices
- Circulant matrices
- Wigner-type matrices
- Balanced Toeplitz and Hankel matrices
- Patterned band matrices
- Triangular matrices
- Joint convergence of i.i.d. patterned matrices
- Joint convergence of independent patterned matrices
- Autocovariance matrix
Empirical and limiting spectral distribution
Moment method
A metric for probability measures
Patterned matrices: A unified approach
Exercises
Wigner matrix
Toeplitz and Hankel matrices
Reverse Circulant matrix
Symmetric Circulant and related matrices
Additional properties of the LSDs
Exercises
A unified setup
Aspect ratio y = 0
Aspect ratio y = 0
Exercises
Normal approximation
Circulant matrix
k-Circulant matrices
Exercises
Wigner-type matrix
Exercises
Main results
Exercises
LSD for band matrices
Proof
Exercises
General pattern
Triangular Wigner matrix
Non-commutative probability space
Joint convergence
Nature of the limit
Exercises
Definitions and notation
Joint convergence
Freeness
Sum of independent patterned matrices
Proofs
Exercises
Preliminaries
Main results
Proofs
Exercises
