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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."

"Dalam konteks matematika komputasi, tensor sering dipandang sebagai larik multidimensi, dengan jumlah dimensinya disebut sebagai orde tensor tersebut. Tensor dapat digunakan untuk merepresentasikan berbagai jenis data, seperti data gambar dan data psikometri. Salah satu masalah yang penting dalam komputasi tensor adalah aproksimasi rank rendah tensor. Untuk sebuah tensor A, masalah aproksimasi rank rendah adalah mencari tensor B yang nilainya paling mendekati tensor A tetapi memiliki rank tertentu yang lebih kecil dari rank A. Untuk tensor orde 2 (matriks), Teorema Eckart-Young-Mirsky menjelaskan bahwa masalah aproksimasi rank rendah matriks dapat diselesaikan dengan dekomposisi nilai singular (SVD). Akan tetapi, memperumum Teorema Eckart-Young-Mirsky untuk tensor adalah sebuah persoalan yang rumit. Masalah utamanya adalah, dalam kasus tensor, ada beberapa definisi rank yang berbeda. Masing-masing definisi rank dihasilkan dengan memperumum sifat-sifat tertentu dari fungsi rank matriks dan dapat menghasilkan nilai yang berbeda-beda untuk tensor yang sama; permasalahan tersebut adalah pokok bahasan skripsi ini. Skripsi ini dimulai dengan membahas konsep-konsep dasar dalam komputasi tensor. Lalu, akan dibahas mengenai tiga definisi konsep rank tensor. Untuk masing-masing definisi rank tensor, akan dipaparkan dekomposisi tensor yang berkaitan; dekomposisi-dekomposisi tensor ditujukan untuk memperumum SVD. Lalu, konsep rank dan dekomposisi tensor digabungkan dalam pembahasan masalah aproksimasi rank tensor. Pembahasan dilanjutkan dengan pembahasan hasil kali *M. Hasil kali *M dibuat untuk membentuk sebuah kerangka umum sebagai upaya menggabungkan beberapa dekomposisi tensor yang telah dibahas sebelumnya. Terakhir, dijelaskan mengenai berbagai sifat dan keunggulan teoretis kerangka hasil kali *M.

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In the context of computational mathematics, tensors are often viewed as multidimensional arrays, with the number of dimensions referred to as the order of the tensor. Tensors can be used to represent various types of data, such as image data and psychometric data. One important problem in tensor computation is the low-rank approximation of tensors. For a tensor A, the low-rank approximation problem is to find the tensor B whose entries are closest to the tensor A but has a certain rank that is smaller than the rank of A. For tensors of order two (matrices), the Eckart-Young-Mirsky theorem says that the matrix low-rank approximation problem can be solved by truncating its singular value decomposition (SVD). However, generalizing the Eckart-Young-Mirsky theorem to tensors is a complicated problem. The main problem is that there are several different definitions of rank in the case of tensors. Each definition of rank is generated by generalizing certain properties of the matrix rank and can yield different values for the same tensor; that problem is the subject of this thesis. This thesis begins by discussing the basic concepts of tensor computation. Then, three definitions of the concept of rank tensor will be addressed. For each definition of rank tensor, the corresponding tensor decomposition is presented; the tensor decompositions are intended to generalize the SVD. Then, the concepts of rank and tensor decomposition are combined to discuss the rank tensor approximation problem. The discussion continues with the discussion of the product of *M. The product of *M is made to form a general framework as an attempt to combine several tensor decompositions that have been discussed previously. Finally, various properties and theoretical advantages of the *M product framework are explained."