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2021-07-04 21:24:33 +0200 commented answer How to construct the set of all symmetric invertible $\{0,1\}$ matrices of order 5 in sagemath

I tried to compile. for that I copied the text, but the outcome is not coming

2021-07-04 20:44:35 +0200 commented answer How to construct the set of all symmetric invertible $\{0,1\}$ matrices of order 5 in sagemath

Nice answer. Thank you. Now from this collection, we we find those invertible matrices whose inverses have entries in {0

2021-07-04 20:42:24 +0200 marked best answer How to construct the set of all symmetric invertible $\{0,1\}$ matrices of order 5 in sagemath

How to construct the set of all symmetric invertible {0,1} matrices (that is, entries of the matrices are either 0 or 1) of order 5 in sage math.

2021-07-03 08:05:26 +0200 asked a question How to construct the set of all symmetric invertible $\{0,1\}$ matrices of order 5 in sagemath

How to construct the set of all symmetric invertible $\{0,1\}$ matrices of order 5 in sagemath How to construct the set

2021-07-01 20:04:08 +0200 edited question Consider the set of all symmetric matrices of a given size $n$ with entries lying in $\{0,1\}$ such that all diagonal entries are zeros in the matrices.

Consider the set of all symmetric matrices of a given size $n$ with entries lying in $\{0,1\}$ such that all diagonal en

2021-07-01 20:03:18 +0200 edited question Consider the set of all symmetric matrices of a given size $n$ with entries lying in $\{0,1\}$ such that all diagonal entries are zeros in the matrices.

Consider the set of all symmetric matrices of a given size $n$ with entries lying in $\{0,1\}$ such that all diagonal en

2021-07-01 20:02:46 +0200 asked a question Consider the set of all symmetric matrices of a given size $n$ with entries lying in $\{0,1\}$ such that all diagonal entries are zeros in the matrices.

Consider the set of all symmetric matrices of a given size $n$ with entries lying in $\{0,1\}$ such that all diagonal en

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2021-04-22 21:10:08 +0200 commented question Matrix solutions to $A^k + B^k = C^k$

actually n is strictly greater than 2 and none of A,B,C are non zero and non nilpotent matrix

2021-04-22 20:03:16 +0200 edited question Matrix solutions to $A^k + B^k = C^k$

Does there exists any triple $(A,B,C)$ of $n\times n$ matrices with integer entries which satisfies $A^k+B^k=C^k$ for at

2021-04-22 20:03:04 +0200 edited question Matrix solutions to $A^k + B^k = C^k$

Does there exists any triple $(A,B,C)$ of $n\times n$ matrices with integer entries which satisfies $A^k+B^k=C^k$ for at

2021-04-22 20:02:36 +0200 asked a question Matrix solutions to $A^k + B^k = C^k$

Does there exists any triple $(A,B,C)$ of $n\times n$ matrices with integer entries which satisfies $A^k+B^k=C^k$ for at

2021-04-07 23:02:52 +0200 commented answer How to construct a class of matrices satisfying a given matrix equation.

Sorry, I was making a mistake.. It is now coming very nicely. Thank you

2021-04-07 23:02:46 +0200 marked best answer How to construct a class of matrices satisfying a given matrix equation.

image description

Here we know that $A=I_n$ satisfies the given matrix equation. But can we find other non trivial matrix ($\neq I_n$). In other words, can we construct a class of matrices satisfying the given matrix equation.

Please help regarding this.

2021-04-07 16:25:18 +0200 commented answer How to construct a class of matrices satisfying a given matrix equation.

def compA(7,5,4,3): assert 5^2 == 4^2 + 3^2 R.<x> = PolynomialRing(ZZ) f = 5^2x^(5^2) - 4^2x^(4^2) - 3

2021-04-07 12:18:22 +0200 commented answer How to construct a class of matrices satisfying a given matrix equation.

Thank you for your answer. But there is no output of this programme when I compile it in Sage

2021-04-05 19:25:57 +0200 commented question How to construct a class of matrices satisfying a given matrix equation.

but p and q both can not be even since r is given to be odd and they form Pythagorean triple

2021-04-05 07:28:12 +0200 edited question How to construct a class of matrices satisfying a given matrix equation.

How to construct a class of matrices satisfying a given matrix equation. Here we know that $A=I_n$ satisfies the give

2021-04-05 07:27:51 +0200 edited question How to construct a class of matrices satisfying a given matrix equation.

How to construct a class of graphs satisfying a given matrix equation. Here we know that $A=I_n$ satisfies the given

2021-04-04 22:59:58 +0200 commented question How to construct a class of matrices satisfying a given matrix equation.

Please help..here p,q,r,n are all given to us..

2021-04-04 16:06:55 +0200 asked a question How to construct a class of matrices satisfying a given matrix equation.

How to construct a class of graphs satisfying a given matrix equation. Here we know that $A=I_n$ satisfies the given

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2020-12-26 16:57:22 +0200 asked a question Consider the class of all possible connected simple graphs on $n$ vertices

Consider the class of all possible connected simple graphs on $n$ vertices ($n$ is any natural number, we can choose any natural number). Now from this collection, can we find those graphs (if there exists any) satisfying the following property: Suppose that $A$ denotes the usual $(0,1)$ adjacency matrix of a graph. Now can we find those graphs explicitly (if there is any) on $n$ vertices such that if $\lambda$ is an eigenvalue of $A$, then $\dfrac{1}{\lambda}$ is also an eigenvalue and if $\alpha$ is another eigenvalue (distinct from $\lambda$), then $-\dfrac{1}{\alpha}$ is an eigenvalue. Basically eigenvalues of $A$ are of the form $(\lambda,\dfrac{1}{\lambda})$ and $(\alpha,-\dfrac{1}{\alpha})$.

Basically I am trying to find the graphs for which some roots of the form $(\lambda,\dfrac{1}{\lambda})$, and some roots of the form $(\alpha,-\dfrac{1}{\alpha})$.

please help regarding this problem

2020-12-24 17:10:25 +0200 commented answer Graphs on 6 vertices with eigenvalue condition

This is a very nice answer. Thank you

2020-12-23 22:25:05 +0200 asked a question Graphs on 6 vertices with eigenvalue condition

Consider the class of all possible connected simple graphs on $6$ vertices. Now from this collection, can we find those graphs (if there exists any) satisfying the following property: Suppose that $A$ denotes the usual $(0,1)$ adjacency matrix of a graph. Now can we find those graphs explicitly (if there is any) on $6$ vertices such that if $\lambda$ is an eigenvalue of $A$, then $\dfrac{1}{\lambda}$ and $-\dfrac{1}{\lambda}$ both are eigenvalues. Simply the question can be said as: Characterize all possible simple connected graphs on $6$ vertices such that if $\lambda$ is an eigenvalue of $A$, then $\dfrac{1}{\lambda}$ and $-\dfrac{1}{\lambda}$ both are eigenvalues.

please help regarding this problem.

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2020-06-25 01:01:46 +0200 marked best answer How to obtain the graph having highest algebraic connectivity?

for G in graphs.nauty_geng("10-c"):

if G.size()==11:

L = G.laplacian_matrix().eigenvalues()

L.sort()

show(L)

G.show()

Using this code I have obtained the connected graphs on 10 vertices with 11 edges. Also I have obtained the Laplacian eigenvalues also for the corresponding graphs. The second smallest eigenvalue of Laplacian matrix is called the algebraic connectivity. Now among all these graphs, I need those graphs which have highest algebraic connectivity among all the graphs on 10 vertices with 11 edges. How we can do that?