Antisymmetric and transitive using the matrix?

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big.bangs
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antisymmetric and transitive using the matrix??

I know about find reflexive and symmetric using the matrix

For example, {1,2,3,4,5}

1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1 (This is reflexive)

1 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 1 (This is not reflexive cause 3 is not R 3)

0 1 0 1 0
1 0 0 0 0
0 0 0 0 1
1 0 0 0 0
0 0 1 0 0 (This is symmetric)

0 1 0 1 0
0 0 1 0 1
0 1 0 1 0
1 0 1 0 0
0 1 0 0 0 (This is not symmetric cause 1R2, but 2 is not R 1)

I calculate the symmetric is start from the row 1, and then check each column in the row 1, after finished all the column in row 1, then i will move on to the row 2.

And my question is how to check the antisymmetric and transitive using the matrix??
 
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big.bangs said:
I know about find reflexive and symmetric using the matrix

For example, {1,2,3,4,5}

1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1 (This is reflexive)

1 0 0 0 0
0 1 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 1 (This is not reflexive cause 3 is not R 3)

0 1 0 1 0
1 0 0 0 0
0 0 0 0 1
1 0 0 0 0
0 0 1 0 0 (This is symmetric)

0 1 0 1 0
0 0 1 0 1
0 1 0 1 0
1 0 1 0 0
0 1 0 0 0 (This is not symmetric cause 1R2, but 2 is not R 1)

I calculate the symmetric is start from the row 1, and then check each column in the row 1, after finished all the column in row 1, then i will move on to the row 2.

And my question is how to check the antisymmetric and transitive using the matrix??

Your questions are incomprehensible. You are using the words "reflexive", "transitive", etc., in seemingly unusual ways. It is not clear to me that your meaning of these words is the same as what I (and many others) would think. So, first, just explain what YOU mean by reflexive, transitive, etc. Then, once we understand what you want to do we will be better able to help.

RGV
 

1. What is antisymmetric and transitive using the matrix?

Antisymmetric and transitive using the matrix is a mathematical concept used to describe the properties of a relation between two objects. It refers to a relation that is both antisymmetric and transitive, meaning that if there is a relation between two objects A and B, then there can be no relation between B and A, and if there is a relation between A and B and between B and C, then there must also be a relation between A and C.

2. How is antisymmetry represented in a matrix?

In a matrix, antisymmetry is represented by having zeros on the diagonal and opposite values in the upper and lower triangles. For example, if A and B are related, then the value at (A,B) in the matrix would be 1, but the value at (B,A) would be -1. This ensures that there can be no relation between B and A.

3. What is an example of a matrix that is both antisymmetric and transitive?

An example of a matrix that is both antisymmetric and transitive is the identity matrix. This matrix has zeros on the diagonal and ones in all other positions, meaning that there can be no relation between any two objects except for each object with itself.

4. How can you determine if a matrix is both antisymmetric and transitive?

To determine if a matrix is both antisymmetric and transitive, you can check if it has zeros on the diagonal and opposite values in the upper and lower triangles. You can also check if the matrix satisfies the definition of antisymmetry and transitivity mentioned in the first question.

5. What is the significance of antisymmetric and transitive matrices in mathematics?

Antisymmetric and transitive matrices are important in mathematics because they are often used to represent relationships between objects in various fields such as graph theory, computer science, and social sciences. They also have applications in solving mathematical equations and systems.

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