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Useful keyboard shortcuts for MS Word

October 28, 2016

workable for Office 365

  • add bullet: control+shift+L
  • clear formatting: control+shift+N

Microsoft Word 2016 Autocorrection English

October 27, 2016

If you would like to change the languarate that the autocorrection is based on,

Review tab->Langurage->Set proofing languarage->Change the language from British to American and disable “Detect language automatically” (your computer is British)

You may also need to go to

File tab->Options->Language->Choose Editing language: from British to American English

Matlab cell, legend

July 22, 2016

str={};
for i=1:n
str=[str, strcat(‘idx=’,num2str(i))];
end
legend(str, ‘location’,’SouthWest’)

Read more…

Relation between eigenvalue and singular value

July 11, 2016

For any square matrix A, we have

-\sigma_{n-k+1}(A) \le \lambda_k\left(\frac{A+A^T}{2}\right) \le \sigma_k(A)

where 0\le\sigma_n\le\dots\le\sigma_1 are the singular values, and \lambda_n\le\dots\le \lambda_1 are the eigenvalues.

Proof of the right half of the inequality:

See Topics in matrix analysis: page 151, Corollary 3.1.5

Proof of the left half of the inequality:

First, we have

\lambda_k\left(\frac{-A-A^T}{2}\right)=-\lambda_{n-k+1}\left(\frac{A+A^T}{2}\right)

To verify, it is easy to see \lambda_1\left(\frac{-A-A^T}{2}\right)=-\lambda_{n}\left(\frac{A+A^T}{2}\right) and \lambda_n\left(\frac{-A-A^T}{2}\right)=-\lambda_{1}\left(\frac{A+A^T}{2}\right).

Second, applying the right half of the inequality gives

\lambda_k\left(\frac{A+A^T}{2}\right)=-\lambda_{n-k+1}\left(\frac{-A-A^T}{2}\right)\ge-\sigma_{n-k+1}(-A)=-\sigma_{n-k+1}(A)

Matlab mod

June 29, 2016

if you would like to achieve something like this:

1 2 3 4->1 2 3 4

-1 0->2 4

5 6->1 2

you should use

mod(i-1,n)+1

where n=4

Graphical meaning of power of adjacency matrix

June 6, 2016

Untitled

Set default initial page view in adobe reader

May 23, 2016

It’s not that easy, but I finally fixed it.

There are three options provided by Adobe Reader.

  1. File->properties->Initial view
  2. Edit->preferences->Page display->Default layout and zoom
  3. Edit->preferences->Accessibility->Override page display

Many people recommend the second way, but it does not work for me.

The first option works, but only for one single PDF.

The third one works for all PDF for me!!! I found it here

http://superuser.com/questions/349971/how-do-i-set-default-view-preferences-in-adobe-acrobat