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**Physics, Astronomy & Cosmology / Re: Who understands the matrix equation Ax=b?**

« **on:**19/01/2016 17:33:03 »

Quote from: TheBox

I can not think where anywhere in my life would have a need to know your equation.Have you ever played a 3D computer game? Or watched just about any film made in the past 20 years? Or used a cellphone, or a WiFi hotspot?

Modern computer graphics makes extensive use of matrices of x, y, z points to represent the shape of every object on the screen. Every time you move in the game, or the camera pans in the film, the GPU does millions (or billions) of matrix operations to transform the location of each point in the scene to its new location on the screen.

Modern wireless telecommunications makes use of multiple antennas in your cellphone, computer, WiFi hotspot and mobile base station. To work out what is the best way to transfer data over these multiple possible paths requires "channel state estimation", which involves solving matrix equations such as those described by Jeffrey.

If you are moving while talking or browsing or using social media (or other people around you are moving), these matrix equations must be solved many times per second to maximize the quantity of data transferred, and minimize delays.

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I know some other maths such as F=ma which I wanted to learn.Single numbers like m in the above equation are called "scalars", and they obey the arithmetic we were taught in primary school and high school.

In junior high-school physics, F and a were also represented as scalars, which is fine if the force and acceleration are all in a straight line. But real forces don't operate in a straight line - think of the forces on billiard balls, which move in a 2 dimensional space, or a planet which moves in a 2D elliptical orbit around its star.

Real cars, planes, spaceships, buildings and bridges operate in a 3 dimensional world, where forces can come from any direction, so scalars are not sufficient for real applications. In these applications, F and a are represented as vectors, and their interactions are represented as matrices.

Matrix arithmetic is an extension of high-school scalars, but "grown up" to work in the real world. I was taught this at university level, but given the ease of calculating with them using computers, I don't see why they couldn't be introduced earlier, these days.

Every time you drive your car over a bridge, or catch a plane, be grateful that

*someone*was able to apply F=ma using matrices.

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