Lx=d: SundayResearch

Here is a follow up of transpose of matrix multiplication.

At one Wednesday night party (meeting), there was a conversation: ``... I met the woman at that party. She was looking for her job...'' ``What does she look like? Pretty? Positive? Tall?'' ``Positive.'' ``I love a positive woman.'' A few minutes later at the same party, ``... I found this matrix in that paper. It was constructed by...'' ``What does the matrix look like? Symmetric? Positive definite? How large?'' ``Positive definite.'' ``I love a positive definite matrix.'' As you see, some of my friends like a positive definite quadratic form matrix. It is also interesting to think about the relationship of this matrix with transpose. But first I would like to talk about transpose only. One of my friend wrote an article `` A mystery of transpose of matrix multiplication -- Why (AB)^T = B^T A^T? '' By the way, it is not comfortable to write a mathematical blog since it is hard to write equations. I have a permission

Reflection lines are lines observed on a surface from tube lights. Car designers employed this to see the surface quality. Usually, parallel fluorescent tubes are placed above the car model. But this is quite common in Germany. This is Berlin Hauptbahnhof (main station). The large part of building is transparent (glass). Steel frames are aligned regularly on the ceiling. These are not fluorescent tubes, but reflection line only requires regularly arranged lines. If there is something specular surface, we could see reflection lines. Please look into the widows of this train. We could easily see that each window has a different quality. Most of the windows did not connects smoothly between windows. Link to the explanation slides References [1] Mario Botsch, Mark Pauly, Leif Kobbelt, Pierre Alliez, Bruno Levy, Stephan Bischo, Christian Roeossl, ``Geometric Modeling based on Polygonal Meshes,'' EG2008 Tutorial, 2008 [2] Takashi Kanai, Yusuke Yasui, ``High-quality Display of Subdi