por Do you know what it is and how we can calculate the rank of a matrix? In this article we will give you a short introduction to this concept.
Rank of a matrix
The rank of an array is the amount of unique information our array contains.
Let’s see a small extension of this explanation, based on an example.
Suppose we have the following matrix:
What do you think is the range of an array like this?
One factor must be taken into account: the first column is linearly dependent on the second. That is to say, If we multiply 2 by the first column, it will give us the values in the third column as a result.
So, we might think about deleting the first column, but if we look closely, the sum of the first three gives us the last one.
Exercise on the rank of a matrix
Imagine that you have been traveling and that you have not had coverage. You arrive home again and have met your friends, but at different times, because none of them agree on a common time.
So:
Friend 1 asks you about your vacation and tells you several things: That his dog has died. That he has found a new job.
Friend 1 has left and friend 2 arrives.
Friend 2 tells you that: He has bought a house. Also that friend 1’s dog has died.
Friend 2 leaves and friend 3 arrives at a different time.
Friend 3 asks you if you know that: Friend 2 has bought a house. He moves to Germany.
So, here is information that is already repeated, such as the purchase of the house and the death of the dog, information shared by various friends.
In this hypothetical case, where we have 6 fields in the matrix, the amount of unique information there is, that is, The rank is not 6, because there is information that other characters have already said, but 4.
The repeated information would be:
That friend 1’s dog has died. That friend 2 has bought a house.
This, mathematically, is expressed by linear dependence. That is, the matrices we have are:
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