My friend, Christopher Ng (who has an electrical engineering degree, is currently an IT project manager, and is also a finance author. Talk about polymathy…) has generously helped me answer that matrix applications and civil engineering question. Let me bring it up again:
How do you picture matrix least-squares method of a traverse adjustment in surveying and in strain-stress material? Tell me about diagonal matrix practical interpretation.
I read through his answer and frankly speaking, and I’m ashamed to say, I don’t quite understand it.
He gave this link first:
Surveys and stress-strain characteristics are two different application domains in civil engineering. I can shed some light on matrices, MLS and stress-strain diagrams.
If you wiki the least squares approach approach [sic], you can find that the generalized problem can be expressed as some sort of a matrix. Solving matrix via quadratic minimization obtains the solution to the least squares problem. Bx = y
If you wiki stress-strain characteristics, it’s simple the physics we used to learn called Hooke’s law. A graph that plots force on the x axis and extension on the y-axis. The least squares approach is just like we do in O level physics, we draw the most probable line that crosses the origin point.
So the picture is that each plot (x,y) can be placed on the matrix and the aim is to draw a line through the points to determine Youngs modulus.
He then went on to explain
The traverse survey occurs when civil engineers take complicated compasses and walk the perimeter of a construction site. They enter the coordinates in bearings and distances traveled into a CAD software system. Ultimately, these engineers are expected to walk to the starting point and trace some kind of loop which is then translated into a map.
The MLS is used to correct errors and adjust the x,y coordinates in a map as there are 3D effects in terrain.
I have no idea how MLS works in this case but you can seek Crandall’s method in your web search to look for graphical examples.
MLS refers to matrix least squares. And O level physics is a physics examination taken by Singaporean students typically at age 16 for entrance towards higher education.
And yeah, what my friend said.