Bijective matrix algebra

Some results on Haar wavelets matrix through linear algebra

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.

Three alternating sign matrix identities in search of bijective proofs

These are rich combinatorial objects with connections to many problems in algebraic combinatorics (see [2], [3], [12]). They also have many different representations. The representation that was used in Kuperberg’s proof of the counting function for alternating sign matrices [9] and Zeilberger’s proof of the refined alternating sign matrix conjecture [14] is the six-vertex model of statistical ...

Bijective proofs of shifted tableau and alternating sign matrix identities

We give a bijective proof of an identity relating primed shifted gl(n)-standard tableaux to the product of a gl(n) character in the form of a Schur function and ∏ 1≤i<j≤n(xi + yj). This result generalises a number of well–known results due to Robbins and Rumsey, Chapman, Tokuyama, Okada and Macdonald. An analogous result is then obtained in the case of primed shifted sp(2n)standard tableaux whi...

Elements of Matrix Algebra

Linear Algebra and Matrix Theory