Let us consider the Bateman or Whittaker's pioneering examples of a Penrose transform. Starting from a holomorphic function on an open subset of twistor space, they constructed a solution to the Laplace equation (in one case in dimension $4$ and in the other case in dimension $3$). Fine, except ...

$\def\F{\Bbb{K}}$ $\def\R{\Bbb{R}}$ Let $\F$ be a field. We can define the Cayley-algebra of dimension $2^n$ over $\F$ by adjoining formal square roots of $-1,$ subject to the constraint that if $e_i$ and $e_j$ are any such square roots then there exists a unique $k$ so that $$e_ie_j=e_k,~ e_...

I am currently reading Non-Negative Matrices. By searching internet I have found some of the following books: (Encyclopedia of mathematics and its applications 64) R. B. Bapat, T. E. S. Raghavan- Nonnegative Matrices and Applications-Cambridge University Press (1997). (Classics in applied mathe...

1.a symmetric matrix in $\mathbb{M}_n(\mathbb{R})$ is said to be non-negative definite if $x^Tax≥0$ for all (column) vectors $x\in \mathbb{R}^n$. Which of the following statements are true? (a) If a real symmetric $n\times n$ matrix is non-negative definite, then all of its eigenvalues are non-ne...

A symmetric matrix in $\mathbb{M}_n(\mathbb{R})$ is said to be non-negative definite if $x^TAx≥0$ for all (column) vectors $x \in \mathbb{R}^n$. Which of the following statements are true? a. If a real symmetric $n×n$ matrix is non-negative definite, then all of its eigenvalues are non-negative. ...

I am doing my Phd in Linear algebra and I am looking for a good book for non-negative matrix theory which will help me to understand the nuts and bolts of the subject. If there is any one book from this question, I will be happy. Infact, if there is any video tutorials on nonnegative matrix the...