A linear transformation from vector space to another can be represented as a matrix. This close relationship between the matrix and is helpful for study of matrices. In this paper, tensor regarded generalization viewpoint instead quadratic form in theory; we discuss some operations present definitions theorems related tensors. For example, provide triangular eigenvalue tensor, QR decomposition ...

In this paper, we give a sufficient condition for the linear transformation preserving the strong q-log-convexity. As applications, we get some linear transformations (for instance, Morgan-Voyce transformation, binomial transformation, Narayana transformations of two kinds) preserving the strong q-log-convexity. In addition, our results not only extend some known results, but also imply the str...

We present the linear loop transformation framework which is the formal basis for state of the art optimization techniques in restructuring compilers for parallel machines. The framework uniies most existing transformations and provides a systematic set of code generation techniques for arbitrary compound loop transformations. The algebraic representation of the loop structure and its transform...

Measurements of the magnitude or duration of physical phenomenon have the property that they are positive and continuous, except for the possibility of exact zeroes when the phenomenon does not occur. Such data cannot be transformed to normality by power transformations or any other means, and special treatment of the zero observations is usually required. The approach of this paper is to model...

We consider the estimation of linear transformations aligning a known binary shape and its distorted observation. The classical way to solve this registration problem is to find correspondences between the two images and then compute the transformation parameters from these landmarks. Here we propose a unified framework where the exact transformation is obtained as the solution of either a poly...

Much of this section was copied and paraphrased from Heath’s Scientific Computing. Anyways. Suppose we are looking for an orthogonal transformation that annihilates desired components of a given vector. Recall that a square real matrix Q is said to be orthogonal if its columns are orthonormal, that is, that Q Q = I. Orthogonal transformations are nice because they preserve Euclidean norms of an...

This paper proposes a technique for solving a Fuzzy Linear Programming Problem(FLPP) when some of its constraints are fuzzy homogeneous. Using these fuzzy homogeneous constraints a fuzzy transformation matrix is constructed. This fuzzy transformation matrix transforms the given problem in to another FLPP with fewer fuzzy constraints. A relationship between these two problems, which ensures that...

Rotations are essential transformations in many parts of numerical linear algebra. In this paper, it is shown that there exists a family of matrices unitary with respect to an orthosymmetric scalar product J , that can be decomposed into the product of two J-unitary matrices—a block diagonal matrix and an orthosymmetric block rotation. This decomposition can be used for computing various one-si...