5 Interesting Facts of Matrix Calculus

Matrix calculus is the extension of calculus to vector or matrix setting. I used to suffer a lot with matrix calculus in my early grad life. I’ve seen some other people to suffer as well. It primarily happens because the standard courses in linear algebra do not cover this topic very often. However, all the maths in Matrix calculus are basically trivial. Anyway, here are a few interesting facts that made my life much easier. I could use these to derive many expressions (e.g. calculating gradients in SGD based algorithms etc.) in my machine learning practice. Check if they can help you or not.

Fact 1

Inside trace, objects (both vector and matrix. tensor?) can cycle or can take transpose of itself. For example:

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Definition of “Usually”

It is a pain to talk with people suffering from superiority complex. The hard work that is vital for acquiring knowledge often brings a delusion of grandeur to some people. They often think that only they can talk in perfect English. Everyone else’s English is just imprecise and bogus. Many of them also show a demeaning attitude. Whenever you’ll say something, they’ll try to point out how your sentence construction is syntactically wrong or mathematically imprecise. Once I met such a delusional person who had some kind of enmity with the word “usually”.

I must concede that I, sometimes, use this word a little too much. But that does not mean that “usually” is imprecise or unscientific. It is possible to put precise mathematical definition for this word. I am writing this definition here; so that, when next time someone would try to confront me with the imprecision of this word, I can gladly point to this article 🙂 :

Usually <some_event>  means the probability of the occurrence of that event is greater than the probability of not occurring that event. In mathematical notation, \text{Usually}(x): p(x)>p(\neg x). For example, “usually it rains here” means p(E)>p(\neg E), where E is the event of raining here.

 

No Rule other than Just Not Hurting Others?

Recently, I was engaged in a long argument in Facebook on what should be the extent of laws in a country. I was defending an argument similar to the one written in the title. I think I came up with some really interesting logic against the proposition. I’m preserving these here. As it was a part of an ongoing conversation, it might sound awkward. The full conversation is available in this Facebook post. Check out the replies of the second comment.

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Teaching Style: Where Many Computer Scientists and Mathematicians Do it Wrong

There is a difference between programming and teaching. I have seen a lot of good programmers to be horrible teacher. In my opinion, this happens when people becomes delusional in thinking that teaching is just like writing programs — tell each and every step, in a logically perfect sequence. In reality, teaching is more than that. First of all, humans don’t need everything to be spelled out. In fact, that is detrimental to teaching (I’ll explain why later). Humans just need broad thick strokes here and there. They are good in connecting the strokes and building perfect picture themselves. In my opinion, the most important objective of teaching should be to generate motivation; not to spell out every detail.

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Digital age or Dark age?

When people used to work with pen and paper, their knowledge used to become a part of the physical world. Once they were deceased, human could still partially access to their thoughts by accessing the papers they scribbled on. Many unpublished articles, personal letters, even drawing and scribbles became part of our history in this way.

What is the condition now for digital age? All the writings we are making in the digital form, how will they survive? What will happen if a great scholar dies and no one knows the password of that scholar’s laptop? Or, what if the medium gets deprecated (imagine the state of floppy disk or Compact Disk) over time and no one knows how to read it? What if the web account gets deleted due to lack of payment? Will it be possible to recover “ancient” scriptures of 2000s when people will live in the 3000s? Will be considered as a dark period of time?Read More »

Instill Pain Endurance?

Should I try to stay in a first world country or should I try to go back to Bangladesh? It is a really difficult question to answer. I’ve been thinking on this sporadically over the last 6 years. There are a lot of selfish reasons for staying in USA, a lot of noble reasons for going back to Bangladesh. But I wanted to find a few solid selfish reasons for going back to Bangladesh. I’ve just found one –> To Instill pain endurance; both for me and my family. Pain endurance is a source of happiness. But to endure pain, one has to suffer from the pain first.

How come pain and sufferings can be a cause of happiness? They are actually not the direct cause, but happiness hides behind the wall of pain and sufferings.

Seeing Professor Gilbert Strang

Today (June 26th, 2015) I went to see one of my favorite teachers — Gilbert Strang.

One day in 2009, while I was watching his Linear Algebra video lectures (http://ocw.mit.edu/…/math…/18-06-linear-algebra-spring-2010/) in a quiet corner of my room, I started to realize that an extra-ordinary beauty was slowly unfolding in front of me. I felt a deep gratitude for this person who introduced me with this beauty. That day I promised, someday, I will see him face-to-face and say “Thank You”. That is exactly what I have done today. This was in my Bucket list for quite some time and now it is checked.

Here is a picture with Prof. Strang. For more, click on the picture.

We haven’t forgotten; we will not forget

As a citizen of Bangladesh, we will not forget the genocide, war-crime, and mass killing of intellectuals (Teachers, Students, Journalists, Doctors, Engineers, Cultural activists) conducted in Bangladesh by Pakistani Army in the name of the religion — Islam. Starting from Operation Searchlight (Conducted in 25th March, 1971 where they massacred the unarmed progressive minds of Dhaka University), Pakistani army killed 3 Million people in just 9 months — one of the greatest atrocities on human after the holocaust.

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