The exponential matrix: an explicit formula by an elementary method

An Extended Matrix Exponential Formula

In this paper we present matrix exponential formulae for the geometric and spectral geometric means of positive definite matrices using a conjectured exponential formula that solved by Wasin So [Linear Algebra Appl. 379 (2004)]. Mathematics subject classification (2000): 15A24, 15A29, 15A48.

An explicit formula for the matrix logarithm

We present an explicit polynomial formula for evaluating the principal logarithm of all matrices lying on the line segment {I(1 − t) + At : t ∈ [0, 1]} joining the identity matrix I (at t = 0) to any real matrix A (at t = 1) having no eigenvalues on the closed negative real axis. This extends to the matrix logarithm the well known Putzer’s method for evaluating the matrix exponential. Key-words...

An Elementary Proof of the Hook Formula

The hook-length formula is a well known result expressing the number of standard tableaux of shape λ in terms of the lengths of the hooks in the diagram of λ. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing more than the fundamental theorem of algebra. This proof was suggested by a q, t-analog of the hook formula given ...

An Explicit Formula for the Free Exponential Modality of Linear Logic

The exponential modality of linear logic associates a commutative comonoid !A to every formula A, this enabling to duplicate the formula in the course of reasoning. Here, we explain how to compute the free commutative comonoid !A as a sequential limit of equalizers in any symmetric monoidal category where this sequential limit exists and commutes with the tensor product. We apply this general r...

An Elementary Method for Computing the Kostka Coefficients