University of Calgary

About Keivan (more)

Keivan Hassani Monfared I am a PIMS postdoctoral fellow in the mathematics and statistics department at University of Calgary, working under supervision of Kris Vasudevan and Mike Cavers and in collaboration with Cam Teskey's lab at Hotchkiss Brain Institute. Prior to this, I was a postdoctoral fellow here under supervision of Peter Lancaster and Alex Brudnyi. I received my PhD (2014) and MSc (2011) from University of Wyoming under supervision of Bryan Shader, and BSc (2009) from Amirkabir University of Technology (Tehran Polytechnic).
Publications Summary: PDF

Research Interests (more)

  • Linear Algebra and Matrix Analysis
  • Combinatorics and Graph Theory
  • Applications in Neuroscience and Economics

Current Teaching (more)

Recently Published or Submitted Papers (more)

  • Inverse spectral problems for linked vibrating systems and structured matrix polynomials
  • Keivan Hassani Monfared and Peter Lancaster: PDF
    • We show that for a given set of $nk$ distinct real numbers \( \Lambda \), and \(k\) graphs on \(n\) nodes, \(G_0, G_1,\cdots,G_{k-1}\), there are real symmetric \(n\times n\) matrices \(A_s\), \(s=0,1,\ldots, k\) such that the matrix polynomial \(A(z) := A_k z^k + \cdots + A_1 z + A_0\) has proper values \(\Lambda\), the graph of \(A_s\) is \(G_s\) for \(s=0,1,\ldots,k-1\), and \(A_k\) is an arbitrary nonsingular (positive definite) diagonal matrix. When \(k=2\), this solves a physically significant inverse eigenvalue problem for linked vibrating systems.
  • A Structured Inverse Spectrum Problem For Infinite Graphs
    Keivan Hassani Monfared and Ehssan Khanmohammadi: PDF
    • It is shown that for a given infinite graph \(G\) on countably many vertices, and a bounded, countably infinite set of real numbers \(\Lambda\) there is a symmetric matrix whose graph is \(G\) and its spectrum is the closure of \(\Lambda\).
  • Existence of a Not Necessarily Symmetric Matrix with Given Distinct Eigenvalues and Graph
  • Keivan Hassani Monfared, Linear Algebra and its Applications: PDF
    • For given distinct numbers \(\lambda_1 \pm \mu_1 \rm{i}, \lambda_2 \pm \mu_2 \rm{i}, \ldots, \lambda_k \pm \mu_k \rm{i} \in \mathbb{C} \setminus \mathbb{R}\) and \(\gamma_1, \gamma_2, \ldots, \gamma_l \in \mathbb{R}\), and a given graph \(G\) with a matching of size at least \(k\), we will show that there is a real matrix whose eigenvalues are the given numbers and its graph is \(G\). In particular, this implies that any real matrix with distinct eigenvalues is similar to a real, irreducible, tridiagonal matrix.
  • The nowhere-zero eigenbasis problem for a graph
    Keivan Hassani Monfared and Bryan L. Shader, Linear Algebra and its Applications: PDF.
    • Using previous results and methods, it is shown that for any connected graph \(G\) on \(n\) vertices and a set of \(n\) distinct real numbers \(\Lambda\), there is an \(n\times n\) real symmetric matrix \(A\) whose graph is \(G\), its spectrum is \(\Lambda\), and none of the eigenvectors of \(A\) have a zero entry.

Recent or Upcoming Talks (more)

  1. Counting to infinity - July 2017
    High School Math Camp at University of Calgary, Calgary, AB, Canada
  2. Using the Jacobian method to solve several inverse eigenvalue problems for graphs - July 2016
    20th Conference of the International Linear Algebra Society (ILAS), Leuven, Belgium
  3. Some Inverse Eigenvalue Problems for Graphs - May 2016
    Western Canada Linear Algebra Meeting (WCLAM),The University of Manitoba, Winnipeg, MB, Canada


JMM 18

We are organizing an AMS special session on Emerging Topics in Graphs and matrices at the Joint Mathematics Meeting 2018, in San Diego, CA. Check out the schedule and plan to attend some of the great talks. It is going to be a great session.

Contact Info

Mailing Address:
Department of Mathematics and Statistics, MS 472
University of Calgary
2500 University Dr. NW
Calgary, Alberta, Canada
T2N 1N4

Office: Math Sciences (MS) 584

email: keivan.hassanimonfar [at]

Find me on

Research Gate: Keivan Hassani Monfared
Google Scholar: k1monfared

My Erdős Number


List of people with Erdős number 2: link