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"Matrix Analysis for Scientists and Engineers provides a blend of undergraduate- and graduate-level topics in matrix theory and linear algebra that relieves instructors of the burden of reviewing such material in subsequent courses that depend heavily on the language of matrices. Consequently, the text provides an often-needed bridge between undergraduate-level matrix theory and linear algebra and the level of matrix analysis required for graduate-level study and research. The text is sufficiently compact that the material can be taught comfortably in a one-quarter or one-semester course.Throughout the book, the author emphasizes the concept of matrix factorization to provide a foundation for a later course in numerical linear algebra. The author addresses connections to differential and difference equations as well as to linear system theory and encourages instructors to augment these examples with other applications of their own choosing."

"Long considered to be a classic in its field, this was the first book in English to include three basic fields of the analysis of matrices -- symmetric matrices and quadratic forms, matrices and differential equations, and positive matrices and their use in probability theory and mathematical economics. Written in lucid, concise terms, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods. Originally published in 1970, this book replaces the first edition previously published by SIAM in the Classics series. Here you will find a basic guide to operations with matrices and the theory of symmetric matrices, plus an understanding of general square matrices, origins of Markov matrices and non-negative matrices in general, minimum- maximum characterization of characteristic roots, Krnoecker products, functions of matrices, and much more. These ideas and methods will serve as powerful analytical tools. In addition, this volume includes exercises of all levels of difficulty and many references to original papers containing further results. The problem sections contain many useful and interesting results that are not easily found elsewhere. A discussion of the theoretical treatment of matrices in the computational solution of ordinary and partial differential equations, as well as important chapters on dynamic programming and stochastic matrices are also included."

"Control Perspectives on Numerical Algorithms and Matrix Problems organizes the analysis and design of iterative numerical methods from a control perspective. The authors discuss a variety of applications, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems, support vector machines, integration and shooting methods for ordinary differential equations, matrix preconditioning, matrix stability, and polynomial zero finding."

""The thoroughly revised and updated second edition of this acclaimed text has several new and expanded sections and more than 1,100 exercises"--"

"Skema pembagian rahasia adalah teknik untuk membagi data rahasia menjadi n bagian dengan menggunakan threshold k, n, dimana partisipan dapat dengan mudah merekonstruksi rahasia jika diketahui minimum k bagian, tetapi pengetahuan dari k-1 bagian tidak dapat mengurai rahasia. Skema pembagian rahasia ini diperkenalkan oleh Shamir pada tahun 1979. Permasalahan pada skema pembagian rahasia Shamir adalah tidak tersedianya cara untuk melakukan verifikasi bahwa dealer terbukti jujur dalam membagikan rahasia, dan bagian dari rahasia terbukti valid, begitu juga dengan skema pembagian rahasia pada gambar yang diajukan oleh Thien dan Lin, atau metode konstruksi menggunakan matriks proyeksi yang dipublikasikan oleh Li Bai. Di sisi lain, sebuah protokol yang dikembangkan disebut skema pembagian rahasia yang diverifikasi memperbolehkan setiap partisipan melakukan validasi terhadap bagian rahasia yang diterima, untuk memastikan autentikasi dari rahasia. Sebuah gambar watermark berukuran m x m akan digunakan untuk menentukan akurasi dari gambar hasil rekonstruksi. Berdasarkan permasalahan di atas, pada skripsi ini akan dibahas skema pembagian rahasia yang diverifikasi, dimana matriks proyeksi digunakan untuk mengkonstruksi bagian rahasia dan matriks publik dari gambar watermark. Gambar rahasia akan direpresentasikan dalam sebuah matriks persegi, dan gambar watermark digunakan untuk autentikasi, dimana hasil rekonstruksi gambar watermark menjamin akurasi dari hasil rekonstruksi gambar rahasia.

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Secret sharing scheme is a technique to share secret data into n pieces based on a simple k, n threshold scheme. Participants will easily reconstruct the secret if there are minimum k pieces, while knowledge of any k-1 pieces of shares will not be able to decipher the secret. This scheme is introduced by Shamir in 1979. The problem with Shamirs secret sharing scheme is the scheme do not provide any way to verify that the dealer is honest and the shares are indeed valid. Thien and Lin proposed image secret sharing in 2002, and Bai proposed construction scheme using matrix projection in 2006, but both of the schemes do not solve the existing problem. On the other hand, a developed protocol for secret sharing called verifiable secret sharing allows every participant to validate their received piece to confirm the authenticity of the secret. An m x m watermark image is used to verify the accuracy of the reconstructed image. Based on the explanation above, this thesis discuss a proposed scheme based on verifiable secret sharing, in which the matrix projection is used to create image shares and a public matrix from watermark image. The secret are represented as a square matrix, the watermark image is used for verifiability, where the reconstructed watermark image verifies the accuracy of reconstructed secret image."