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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

14 votes
1 answer
731 views

For a stable matrix $B$ and anti-symmetric $T$, such that $B(I+T)$ is symmetric, show that $...

Let stable matrix (i.e., its eigenvalues have negative real parts) $B \in \mathbb R^{n \times n}$ and anti-symmetric matrix $T \in \mathbb R^{n \times n}$ satisfy $$B^\top - T B^\top = B + B …
stochastic's user avatar
8 votes
1 answer
2k views

Matrix elements of exponential of tridiagonal matrices

Is there a way to compute one matrix element of the exponential of a tridiagonal matrix without having to compute the rest of the elements? Motivation: I'm trying to find the first passage time d …
stochastic's user avatar