Category Archives: Matrix representation

Correction on the 08 Dec 2015 post; there are two typo’s…

3D complex numbers, Corrections, Matrix representation

It is not a big deal because every person who understands a bit about how matrix representations work sees instantly these must be two typo’s.

But recently about once a week I am scanning how this new website is doing in search engines like Google. And I am very satisfied, every post can now pop up as a separate search result and for example on pictures to my surprise the next picture popped up as pic number six if you search for ‘3d complex numbers’.
This is the version with the two typo’s in it:

0002=02Dec2015=teaser_6D_complex_numbersAnd here is the corrected version:

0009=02Dec2015=teaser_6D_complex_numbers_corrected

So it is not a big deal but if a search result ends that high it is not unwise to correct it.
And to be honest, I know for years that you can craft let’s say 15 dimensional complex numbers from 3D and 5D complex numbers.
But to be honest, I had never done it until the December update from last year.

And I have learned some stuff too, only if you dive into those technical details like how those basis vectors are actually related you appreciate it so much more.
You know the nicest thing about higher dimensional complex numbers is very simple: I know for sure I am about one of the first humans to hang around in those spaces.
Beside the mathematical beauty the stuff has, it has also that old stuff like discovering new lands that is basically baked into the human genome.

Ok, enough of the phylosofical bla bla. Till updates.

Matrix representations and how to craft them.

3D complex numbers, Matrix representation

Here it is still 01 jan 2016 so a happy new year.
In this update with five pictures with the standard size of 550 by 550 pixels we are going to look at how to craft matrix representations for higher dimensional complex numbers.

It is all rather basic stuff.

Here we go with post number 1 in the year 2016:

0006=01Jan2016=matrix_representation01

 

0006=01Jan2016=matrix_representation02

 

0006=01Jan2016=matrix_representation03

0006=01Jan2016=matrix_representation04

0006=01Jan2016=matrix_representation05

Yeah yeah, every point of this graph represents a 3D complex number that if you craft the matrix representation of it, it is a unitary matrix.

So the next time you see a physics professional professor writing stuff like SU(3) you instantly know you are dealing with some form of idiot life…

Cauchy-Riemann equations for the complex plane and for 3D complex numbers.

3D complex numbers, CR equations, Matrix representation

 

In itself the name of ‘Cauchy-Riemann equations’ is a terrible way of naming these equations because it says nothing about why they are important.

It would be better to name the stuff involved like ‘Chain rule equations for partial derivatives’ because if that would be the case you would understand why these equations are worth your precious time anyway…

This update is 8 pictures of size 550 by 550 pixels or about 5 pages of A4 size if crafted in the A4 size format.
Now why are CR equations important?
Very simple: You can find the derivative of a function just like on the real number system or in the complex plane. That is why CR equations are the basic food for understanding higher dimensional complex number systems…

Enough of the bla bla, here are the 8 pictures:

 

0004=12Dec2015=CR_equations01

 

0004=12Dec2015=CR_equations02

0004=12Dec2015=CR_equations03

0004=12Dec2015=CR_equations04

0004=12Dec2015=CR_equations05

0004=12Dec2015=CR_equations06

0004=12Dec2015=CR_equations07

0004=12Dec2015=CR_equations08

This stuff is basic stuff so it should be hanging out on this new website.

Till update my dear reader.

Eight pages on 6D numbers (containing 3D and 2D complex numbers).

3D complex numbers, Matrix representation

The day before yesterday I finished an 8 page long update on six dimensional complex numbers from the viewpoint of inclusion and extension.

So basically I show that the complex plane and the 3D complex numbers are included in the 6D space while the other way around you can make a 6D space starting with the 2D and 3D complex spaces.
Link:
Inclusion and extension of complex spaces
http://kinkytshirts.nl/rootdirectory/just_some_math/3d_complex_stuff03.htm#06Dec2015

0002=02Dec2015=teaser_6D_complex_numbers

Well well, I still have a long learning curve to do on this new website because you can also make pictures shown at their real size…

Ok, now the previous website has gotten so much attention it would be time to post a bit more stuff in here. After all after just a few weeks and almost no content at all weirdly enough it already ranks relavtively high in the search engine stuff.

Another problem to be solved is that the comment section does not work and even the categories are disfunctional… Very likely this wordpress theme is developed by somebody that has no math insight at all. Why can I make categories while they do not work???
Beat’s me. Anyway, till updates.