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Real
Life Matrix Operations
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| There are several uses for matrices in the real world. You will learn about many in your independent study next year. I am going to show you how a communication matrix works. This is Chapter 14.4 in your book in case you were wondering. Anyway, below is the scenario in which I will teach you how a matrix can be used in communications between ships. |
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| Here is your scenario. Ship A can send a direct message to Ship B and Ship C, Ship B can send direct messages with Ship A and Ship C, Ship C can send direct messages to all of the ships, and Ship D can send direct messages with Ship C. Ship D cannot directly communicate with Ship A, but it can still communicate to Ship A by relaying the message through Ship C. While a diagram is simple for 4 ships, the US Navy has thousands of ships. Imagine the size of that diagram!!! Instead, they use communication matrices. The ships go above the matrix and show the direct communication routes. |
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| Now we have matrix M. The horizontal values
are from ship and the vertical values are to ship. If there is a
1, then direct communication is possible. If you see a 0 as an element,
than direct communication is simply not possible. Notice that the
diagonal values are 0. This is assuming that no ship sends messages
directly to itself. Let’s make a second matrix and call it M2. This will give the number of 2 step indirect communication possibilities. These 2 step indirect communication possibilities are called relays. This is what it looks like. |
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| If we add matrix M and matrix M2, we get the total number of communications (Direct and 2 step relay) that are possible between the two matrices. |
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| There is a brief , but somewhat thorough illustration of matrix communication. |
