I have found the following $n\times n$ squared matrix in one stability analysis problem (i.e. I have to identify the sign of its eigenvalues) $$ A(\theta) = \begin{bmatrix} W(\theta)+W(\theta)^T & -W(\theta) & 0 & \dots & 0 & 0 \\ -W(\theta)^T & W(\theta)+W(\theta)^T & -W(\theta) & \dots & 0 & 0 \\ \vdots & \vdots […]

Problem: Let A be a square matrix with all diagonal entries equal to 2, all entries directly above or below the main diagonal equal to 1, and all other entries equal to 0. Show that every eigenvalue of A is a real number strictly between 0 and 4. Attempt at solution: Since A is real […]

Intereting Posts

What is the equation describing a three dimensional, 14 point Star?
Metrizability of a compact Hausdorff space whose diagonal is a zero set
How to solve this ODE?
Covering space is a fiber bundle
Prove local minimum of a convex function is a global minumum (using only convexity)
Show that $9+9x+3x^3+6x^4+3x^5+x^6$ is irreducible given one of its roots
The Matrix Equation $X^{2}=C$
Polygons with two diagonals of fixed length
Which concepts in Differential Geometry can NOT be represented using Geometric Algebra?
Example of non-homeomorphic compact spaces $K_1$ and $K_2$ such that $K_1\oplus K_1$ is homeomorphic to $K_2\oplus K_2$
Why $\sqrt {-1}\cdot \sqrt{-1}=-1$ rather than $\sqrt {-1}\cdot \sqrt{-1}=1$. Pre-definition reason!
Suppose $f:\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞
Find a binary operation on a set of $5$ elements satisfying certain conditions and which does not define a group
Integrate $\int\sqrt{x+\sqrt{x^{2}+2}} dx$ .
Ergodicity of tent map