# The Matrix Recalculated: This is beautiful

Anyone who’s ever worked with Dijkstra’s algorithm or complex information systems understands matrices, and knows what a PITA they are.  If they weren’t incredibly useful (from computer games to air traffic control), nobody would use them.

This video sounds like propaganda for google’s AI system.  Putting that aside, the reported increase in efficiency of solving matrics is incredible.  Problems on large matrices were always solvable, but took as long as an Ackerman function.  With these shortcuts, large matrices can be solved in reasonable times.

Now if they could just find a shortcut for inverting matrices (e.g. from 3×2 to 2×3).

1. says

So…what real-world application does matrix multiplication have, anyway?

• says

If you use GPS or polygonal FPS games, you’re using it.

• Rob Grigjanis says

Here’s an example in economics

https://en.wikipedia.org/wiki/Matrix_multiplication#Resource_allocation_in_economics

Of course, matrices are indispensable in physics, engineering and other fields, but I just think working with matrices is darn good fun! Yeah, I’m a weirdo.

2. says

>Now if they could just find a shortcut for inverting matrices (e.g. from 3×2 to 2×3).

Do you mean transposing matrices? Usually only square matrices can have inverses.

• Rob Grigjanis says

A mxn matrix M can have a nxm right inverse R if m < n (so that MR =I, where I is the mxm identity matrix), or a nxm left inverse L if m > n (so that LM=I, where I is the nxn identity matrix). But in either case, R and L are not uniquely determined. Think of the trivial case of a 1×2 or 2×1 matrix. Anyway, R and L would be referred to as pseudoinverses.