About wanting to use the Transpose of a matrix, instead of the Inverse.

There is a subject which I’ve mentioned in scant ways, in other postings, but which I have not yet written a posting about, directly.

A situation can arise in which we have a rotation matrix, and where we’d like to invert the rotation it defines, but where the task of actually computing the inverse of the matrix would be too expensive computationally. And so the question can come up, of whether to use the transpose will also work.

The answer is, that in one specific situation the transpose can be used. This is, if each column of the matrix is a unit vector, and if all the columns are mutually orthogonal. If that’s the case, then the determinant of the matrix will also be equal to (1), and the transpose will be equal to the inverse.

Simultaneously, this will then also be true for all the rows of (either) matrix.

Therefore, when I wrote that a Perpendicular matrix could be computed, in case the original matrix defined a quadric, and that the transpose of that perpendicular matrix can be used, as if that was its inverse, I was describing a special situation, in which the perpendicular matrix would have been orthonormal to begin with.

In case a matrix which defines a conversion of coordinates is not orthonormal, then this approach will not work, and its inverse must be used. And I think that the resulting matrix is also called ‘The Jordan Product’ of an original matrix. My exercise did not need this.

Dirk

 

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About the Frame-Rate of Hardware-Accelerated Animations.

One of the subjects which I’ve posted about before, is that in the case of typical hardware-accelerated animations, the frame-rate, which some people just know as ‘the FPS of the animation’, is actually lower than the refresh-rate of the monitor.

Well, if the user is running Plasma 5 as his desktop-manager – which is Linux-based – then he can open ‘System Settings -> Desktop Behaviour -> Desktop Effects’, and he will see a list of available compositing effects, that would all be hardware-accelerated, and under the section of ‘Tools’, there is an effect named ‘Show FPS’. Enabling that effect, and then clicking on ‘Apply’, will cause a piece of OSD information to display, that actually shows the frame-rate. The user will notice that it does not equal the refresh rate of his monitor.

But there is a catch to this. Often, the rendering software will place an upper limit on the frame-rate. Frame-rates actually higher than the refresh rate of the display device accomplish no useful purpose, and there used to be a simple, command-line test which Linux users could run, which was called ‘glxgears’. This would display a very simple animation, of a red, a green and a blue gear, rotating smoothly. In very early versions of this test-program, a frame-rate of something unreasonable, such as 2000 or maybe even 5000 FPS might result, which simply represents a waste of GPU power. The gears would still rotate at the same, correct apparent speed, but each frame-cycle would be fewer than 1 millisecond apart on average. Therefore, more-recent versions of this test-program will cap the frame-rate at the refresh rate of the monitor, and the gears will display as rotating at the same, smooth speed.

Dirk

 

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An update on how to use Latte-Dock.

One of the features which I have posted about recently, is the Plasma 5 add-on called ‘Latte-Dock’. Specifically I wrote, How the user can install version 0.6.0 of this add-on, if it isn’t in the package repositories. What I had also written was, that a safe practice in using Latte-Dock would be, to keep the default Plasma 5 application-launcher in his panel, as a back-up, so that he will always have an application-launcher to click on, even if Latte-Dock crashes.

Well since then I have learned that a more avant-garde way exists to use Latte-Dock, which is, to place the default application-launcher onto the dock as well. This can easily be done because the default application launcher is a widget like any other, which can be dragged to this dock. As an additional detail, a method exists to get v0.6.0 of Latte-Dock to open the application launcher, by just pressing the Super Key, assuming that it has been added to the dock. The instructions I’ve just linked to do not count for later versions of Latte-Dock because those versions already have a check-box in their GUI, which does the same thing.

Hence, I’ve decided to be more progressive in my test-setup for Latte-Dock, and have also placed my only application-launcher onto this dock:

Screenshot_20190329_070015

There is one detail which the reader should note however. I have kept one quick-launcher in the upper-left-hand corner of the screen, in the Plasma panel: The launcher that restarts Latte-Dock from the GUI with one click. The reason I have kept this safeguard is the observation that Latte-Dock can still crash from time to time, which means that the user would be without an application launcher, until he or she gets to restart the dock.

But this way, the layout of that desktop is even more different from the Windows-like layout – common to Plasma 5 and KDE 4 – than it only was a few days ago.

Dirk

 

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Kernel Update Today, Downtime

I take the unusual approach of hosting my site and blog, on my PC at home. This means that if my computer, which I name ‘Phoenix’, has any down-time, so does my blog.

This afternoon, ‘Phoenix’ received a routine kernel update, that seemed to go well. But because even a Linux computer needs a reboot after a kernel update, this site was down briefly, from 12h55 until about 13h15.

On the same note I should mention that yesterday, March 27, we had a power-failure from about 16h00 until 17h45. For that reason as well, my site and blog could not have been on-line.

I apologize for any inconvenience to my readers.

Dirk

 

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