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 2021-06-17 05:00:01 +0200 received badge ● Notable Question (source) 2021-05-18 01:42:23 +0200 received badge ● Popular Question (source) 2021-04-24 08:53:13 +0200 received badge ● Famous Question (source) 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. 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. = 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 2021-03-18 17:24:50 +0200 received badge ● Notable Question (source) 2021-02-01 12:57:50 +0200 received badge ● Famous Question (source) 2020-12-26 21:11:07 +0200 received badge ● Famous Question (source) 2020-12-26 21:11:07 +0200 received badge ● Popular Question (source) 2020-12-26 21:11:07 +0200 received badge ● Notable Question (source) 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. 2020-12-23 22:13:47 +0200 received badge ● Famous Question (source) 2020-10-27 17:10:28 +0200 received badge ● Notable Question (source) 2020-10-08 00:46:26 +0200 received badge ● Notable Question (source) 2020-07-15 14:27:22 +0200 received badge ● Popular Question (source) 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?