This book was done during the course of the author‘s reading ``matrix theory‘‘ by Prof. X.Z. Zhan from 22nd Oct. 2014 to 13th Nov. 2104.

Thank Prof. X.Z. Zhan for the reply of the email; and some hints from Dr. D.M. Zhou, such as

1. the sepctral norm of $A$ is just the largest singular value of $A$.

2. the spectral norm is the smallest unitarily invariant norms, which inspired me in solving Problem 4.9 by using Problem 4.11.

Also, some typos were found during this fun journey in the matrix theory.

1. Page 28, last 2nd line, $\bbC^n$ should be $\bbC^m$.

2. Page 33, last line, $S$ should be $S^T$.

3. Page 44, Problem 3, $i+j-1\leq n$ could just be omitted.

4. Page 58, Fan$k$ should be Fan $k$.

5. Page 75, line 4, the first $W$ should be $U^*$, and the second one should be $V$.

6. Page 81, last 6th line, the largest row sum should be the largest column sum.

7. Page 99, Problem 6, Perron root should be Perron vector.

Sincerely yours, Zujin Zhang

13th, Nov. 2014

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