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Iosif Pinelis
Iosif Pinelis
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Even for the case Rademacher entries, Theorem 2.7.1 does not provide a positive answer to your Question 1, which I think does not have a positive answer at all: I think $C$ cannot be made arbitrarily large; or, at best, radically new, so far unknown methods are needed.

The answer to your Question 2 is positive, in view of Theorem 3.1 and Fact 2.4 (for general subgaussian entries) in the paper by Litvak et al (referred to in the book by Tao that you linked).

Even for the case Rademacher entries, Theorem 2.7.1 does not provide a positive answer to your Question 1, which I think does not have a positive answer at all: I think $C$ cannot be made arbitrarily large; or, at best, radically new, so far unknown methods are needed.

The answer to your Question 2 is positive, in view of Theorem 3.1 and Fact 2.4 (for general subgaussian entries) in the paper by Litvak et al (referred to in the book by Tao that you linked).

The answer to your Question 2 is positive, in view of Theorem 3.1 and Fact 2.4 (for general subgaussian entries) in the paper by Litvak et al (referred to in the book by Tao that you linked).

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Iosif Pinelis
Iosif Pinelis
  • 127.7k
  • 8
  • 107
  • 229

Even for the case Rademacher entries, Theorem 2.7.1 does not provide a positive answer to your Question 1, which I think does not have a positive answer at all: I think $C$ cannot be made arbitrarily large; or, at best, radically new, so far unknown methods are needed.

The answer to your Question 2 is positive, in view of Theorem 3.1 and Fact 2.4 (for general subgaussian entries) in the paper by Litvak et al (referred to in the book by Tao that you linked).