All Questions

Let $M_{n}(\mathbb{Q}) $ denote the $n$ times $n$ matrices over the rational number field. $N$ be a subspace of $M_{n}(\mathbb{Q}) $.Then if all the non-zero matrices in $N$ are invertible, what is ...

What is the maximal number of orthogonal operators $ A _{1} , \dotsc, A _ {m} $ in $ \mathbb{Q}^{ n } $ satisfying the relations $ A_{i}^{2} = - I $ and $ A_{i}A_{j} + A_{j}A_{i} = 0 $ for $ i \neq ...

In a (right) finite dimensional quaternionic Hilbert space there is an analogue of the spectral theorem (see theorem 4.6 in Farenick and Pidkowich) for normal matrices in $\mathbb{H}^{m\times m}$, ...

A quaternionic matrix $A$ gives rise to a function $\mathbb{H}^n \to \mathbb{H}^n$ given by $x \mapsto A \cdot x$. This is real linear, but not complex- or quaternionic-linear (in general) if we ...

I have a number of questions which seem linked to me, about basic (?) linear algebra: Given a field (possibly skew) $K$, and an superfield $L$, one can do linear matrix algebra with coefficients in $...