Answer for matrix applications and civil engineering question

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:
http://answers.yahoo.com/question/index?qid=20091207151537AAYSibI

Then

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.

Help – Matrix applications and civil engineering

I have a problem. One of my readers asked me a question and I don’t have an answer. The question (paraphrased and mangled slightly) is:

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 think my brain exploded after reading it. What in tarnation is a traverse adjustment? Holy smokes, strain-stress material? I have no idea what I was in for…

After weeks of sitting on it, and doing some preliminary research, I’ve decided I can’t answer it. I’m sorry I let you down, O reader who sent me the question. I presume this is related to civil engineering. I know little about it, and I’ll probably spout rubbish if I start answering.

This is where you come in. Help answer the question. You can write it in a comment, or contact me via email. A civil engineering reader gets help, and you get a warm fuzzy feeling of doing something good.

UPDATE: We have an answer.