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Ungraded Matrix Factorizations as Mirrors of Non-orientable Lagrangians
We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds. An ungraded matrix factorization of a...
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Introduction to Matrix Factorizations
This chapter introduces the basic concepts of Gaussian elimination and its formulation as a matrix factorization that can be expressed in a number of...
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Exact QR factorizations of rectangular matrices
QR factorization is a key tool in mathematics, computer science, operations research, and engineering. This paper presents the roundoff-error-free...
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Graded matrix factorizations of size two and reduction
We associate a complete intersection singularity to a graded matrix factorization of size two of a polynomial in three variables. We show that we get...
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Factorizations and eigenvalues of the (r, k)-bonacci matrices
Matrix factorizations brings many conveniences and advantages for solving some real-life problems and for computational processes. The purpose of...
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Sparse LU Factorizations
This chapter considers the LU factorization of a general nonsymmetric nonsingular sparse matrix A. In practice, numerical pivoting for stability...
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Abstract factorization theorems with applications to idempotent factorizations
Let ⪯ be a preorder on a monoid H with identity 1 H and s be an integer ≥ 2. The ⪯-height of an element x ∈ H is the supremum of the integers k ≥ 1...
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Sketch-based multiplicative updating algorithms for symmetric nonnegative tensor factorizations with applications to face image clustering
Nonnegative tensor factorizations (NTF) have applications in statistics, computer vision, exploratory multi-way data analysis, and blind source...
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Algebraic Preconditioners and Approximate Factorizations
When a matrix factorization is performed using finite precision arithmetic, the computed factors are not the exact factors. Despite this, the...
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d-Gaussian Fibonacci, d-Gaussian Lucas Polynomials, and their Matrix Representations
We define d -Gaussian Fibonacci polynomials and d -Gaussian Lucas polynomials and present matrix representations of these polynomials. By using the...
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Sparse Matrix Ordering Algorithms
So far, our focus has been on the theoretical and algorithmic principles involved in sparse Gaussian elimination-based factorizations. To limit the...
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Matrix Factorization Ranks Via Polynomial Optimization
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing...
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Matrix Algebra
The need to understand matrix algebra in the context of underlying applications is paramount. Rank one projections are the building tools and they...
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Matrix Equations
This chapter concentrates on solving the matrix equation $$\textbf{A}\textbf{x} =...
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Factorizations of Characteristic Functions of Iterated Liftings
We obtain a factorization of the characteristic function of a contractive two-step iterated lifting in terms of the characteristic functions of...
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Fast Nonnegative Tensor Factorizations with Tensor Train Model
AbstractTensor train model is a low-rank approximation for multidimensional data. In this article we demonstrate how it can be succesfully used for...
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The full rank expressions for the W-weighted Drazin and core-EP inverse of a matrix and their applications
This paper presents several new expressions for the W -weighted Drazin and core-EP inverse of a matrix based on Urquhart formula. These expressions...