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"This book deals with the application of density matrix theory to atomic and molecular physics. The aim is to precisely characterize sates by a vector and to construct general formulas and proofs of general theorems. The basic concepts and quantum mechanical fundamentals (reduced density matrices, entanglement, quantum correlations) are discussed in a comprehensive way. The discussion leads up to applications like coherence and orientation effects in atoms and molecules, decoherence and relaxation processes. This third edition has been updated and extended throughout and contains a completely new chapter exploring nonseparability and entanglement in two-particle spin-1/2 systems. The text discusses recent studies in atomic and molecular reactions. A new chapter explores nonseparability and entanglement in two-particle spin-1/2 systems."

"This unique book addresses advanced linear algebra from a perspective in which invariant subspaces are the central notion and main tool. It contains comprehensive coverage of geometrical, algebraic, topological, and analytic properties of invariant subspaces. The text lays clear mathematical foundations for linear systems theory and contains a thorough treatment of analytic perturbation theory for matrix functions."

"Kriptografi merupakan ilmu yang mempelajari teknik-teknik matematika yang berhubungan dengan keamanan pesan. Suatu pesan jika hanya disimpan oleh satu orang saja terdapat resiko dimana orang tersebut menyalahgunakan atau memanipulasi pesan. Sedangkan jika terlalu banyak orang yang dapat mengakses pesan, kemungkinan kebocoran pesan menjadi lebih besar. Salah satu studi kriptografi yang digunakan untuk mengatasi masalah ini yaitu skema pembagian rahasia. Skema pembagian rahasia adalah metode mengamankan pesan dengan mendistribusikan pesan tersebut menjadi beberapa bagian kepada partisipan (orang), sedemikian sehingga hanya kombinasi partisipan (orang) tertentu yang dapat membuka isi pesan. Dalam tugas akhir ini dibahas mengenai bagaimana mengkonstruksi skema pembagian rahasia menggunakan matriks proyeksi. Selanjutnya, skema akan diimplementasikan pada pesan berupa string yang diubah ke bentuk kode ASCII (American Standart Code for Information Interchange) dan dapat direpresentasikan sebagai matriks bujur sangkar.

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Cryptography is a study of mathematical techniques related to message security. When a message is only saved by one person, there will be a risk that the person will misuse or manipulate the message. Whereas, when too many peope have access to the message, there will be more possibilities of message to be leaked. One of the ways to overcome this problem is by secret sharing scheme. Secret sharing scheme is a method to secure message by distributing it to participants (people), so that only certain combinations of people can open the message. In this undergraduate thesis, the discussion is focused on how to construct secret sharing scheme by using matrix projection. Then, the scheme will be implemented to message in the form of string which has been changed into ASCII (American Standart Code for Information Interchange) and can represented as a square matrix."

"This thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions--that is, the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the LU and QR decompositions--their computation and applications. The singular value decomposition is also treated, although algorithms for its computation will appear in the second volume of the series. The present volume contains 65 algorithms formally presented in pseudocode. Other volumes in the series will treat eigensystems, iterative methods, sparse matrices, and structured problems. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. To give the series focus, the emphasis is on algorithms, their derivation, and their analysis. The reader is assumed to have a knowledge of elementary analysis and linear algebra and a reasonable amount of programming experience, typically that of the beginning graduate engineer or the undergraduate in an honors program. Strictly speaking, the individual volumes are not textbooks, although they are intended to teach, the guiding principle being that if something is worth explaining, it is worth explaining fully. This has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study."