About: Matrix Chernoff bound

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For certain applications in linear algebra, it is useful to know properties of the probability distribution of the largest eigenvalue of a finite sum of random matrices. Suppose is a finite sequence of random matrices. Analogous to the well-known Chernoff bound for sums of scalars, a bound on the following is sought for a given parameter t:

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  • For certain applications in linear algebra, it is useful to know properties of the probability distribution of the largest eigenvalue of a finite sum of random matrices. Suppose is a finite sequence of random matrices. Analogous to the well-known Chernoff bound for sums of scalars, a bound on the following is sought for a given parameter t: The following theorems answer this general question under various assumptions; these assumptions are named below by analogy to their classical, scalar counterparts. All of these theorems can be found in, as the specific application of a general result which is derived below. A summary of related works is given. (en)
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  • For certain applications in linear algebra, it is useful to know properties of the probability distribution of the largest eigenvalue of a finite sum of random matrices. Suppose is a finite sequence of random matrices. Analogous to the well-known Chernoff bound for sums of scalars, a bound on the following is sought for a given parameter t: (en)
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  • Matrix Chernoff bound (en)
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