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Description
An Introduction to Linear Algebra and TensorsThe present book, a valuable addition to the English language literature on linear algebra and tensors, constitutes a lucid, eminently readable and completely elementary introduction to this field of mathematics. A special merit of the book is its free use of tensor notation, in particular the Einstein summation convention. The treatment is virtually self contained. In fact, the mathematical background assumed on the part of the reader hardly exceeds
The present book, a valuable addition to the English-language literature on linear algebra and tensors, constitutes a lucid, eminently readable and completely elementary introduction to this field of mathematics. A special merit of the book is its free use of tensor notation, in particular the Einstein summation convention. The treatment is virtually self-contained. In fact, the mathematical background assumed on the part of the reader hardly exceeds a smattering of calculus and a casual acquaintance with determinants.The authors begin with linear spaces, starting with basic concepts and ending with topics in analytic geometry. They then treat multilinear forms and tensors (linear and bilinear forms, general definition of a tensor, algebraic operations on tensors, symmetric and antisymmetric tensors, etc.), and linear transformation (again basic concepts, the matrix and multiplication of linear transformations, inverse transformations and matrices, groups and subgroups, etc.). The last chapter deals with further topics in the field: eigenvectors and eigenvalues, matrix ploynomials and the Hamilton-Cayley theorem, reduction of a quadratic form to canonical form, representation of a nonsingular transformation, and more. Each individual section -- there are 25 in all -- contains a problem set, making a total of over 250 problems, all carefully selected and matched. Hints and answers to most of the problems can be found at the end of the book.
Dr. Silverman has revised the text and numerous pedagogical and mathematical improvements, and restyled the language so that it is even more readable. With its clear exposition, many relevant and interesting problems, ample illustrations, index and bibliography, this book will be useful in the classroom or for self-study as an excellent introduction to the important subjects of linear algebra and tensors.
Binding Type: Paperback
Publisher: Dover Publications
Published: 10/18/2010
ISBN: 9780486635453
Pages: 192
Weight: 0.46lbs
Size: 8.24h x 5.62w x 0.39d
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4.4 ★★★★★
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Product Reviews
★★★★★ 5
Fun and filled with facts
Format: Hardcover
Stinkbird is a humorous, kid-centric tale featuring the Amazonian hoatzin bird. It's filled with interesting facts about this stinky bird. Esbaum's distinct, fun voice is inviting, and Shea's illustrations are lush and colorful. Backmatter is engaging and amusing, too! This will be a terrific addition to classrooms, libraries, and home bookshelves.
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Reviewed in the United States on June 14, 2023
★★★★★ 5
READ BEFORE GIVING TO A CHILD
Format: Paperback
Five stars in hopes it is listed at the top.
PLEASE read before you give this to your child! The art work is gorgeous, a very gift able book! I got this for my dragon loving 11yr old as a Christmas book to enjoy in December. Let me just tell you a quick run down of the book.... this child is the only child left unadopted at an orphanage run by a nasty woman and her evil dog. The woman is annoyed by the child and as punishment she cancels Christmas and puts a chain around her ankle and locks her in a dog kennel (yes it says this many times, not simply implied but directly said it and a drawing of it). Finally a little Christmas magic and glimmer of joy when a snow dragon frees her for one quick adventure. That portion is a cute story but it's a very short part in the book. When the adventure is over the child is snuck back in and ankle chain back on and back in the dog kennel. The mean woman returns and says it's time to play a game called "chase".....then the book details what this game is.... this mean woman makes the orphans hold bones and tells them to run, then her evil dog is allowed to chase the kids (scary, not a fun dog frolicking with happy children).....finally at the end the little girl and her sweet dancing dog are adopted. But this book is so sad, this is not a sweet story or Christmas fun. I'm returning the book bc I feel like it will make my child sad instead of enjoy a cute Christmas story. If you are an adoptive parent or a foster parent this may really trigger your children, any child who is sensitive would probably not like this book. However every child is different so for some kids they may be less bothered and just enjoy the dragon and cute last page with the new family walking away together. But read the book for yourself before giving it to a child. I'm 37 with no history of childhood trauma myself and I found this book to be a bit much. I use to be a foster mom and I really wanted to write a review so parents would understand what's in this book bc I almost didn't read it before giving it to my child for Christmas! Glad I read it! The story could have been adorable if they let the dragon be the main part of the story. Not the abuse the child is suffering in the orphanage.
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Reviewed in the United States on November 30, 2025
★★★★★ 5
Lovely Winter Solstice Book
Format: Hardcover, Format: Hardcover
My son loved this winter solstice story! Told by the perspective of the animals, each one brings a little something to share with the others as they decorate a tree together with their items and it's exactly what I wanted in a winter solstice story for my 4 year old. Not too complex which is ideal for younger children, not soly describing the change of season. I feel like this is more of the heart of winter solstice, coming together with friends and family, being generous and having gratitude, and over all sharing light with each other in the longest night of the year. My son's favorite page is definitely the fold out!
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Reviewed in the United States on December 31, 2024
★★★★★ 5
Beautiful illustrations and story!
Format: Hardcover
Christmas/ Solstice gift for grands. The entire family hovered it. Both story and drawings are beautiful
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Reviewed in the United States on February 3, 2025
★★★★★ 5
Beautiful Book
Format: Hardcover
This book is absolutely beautiful. I love the sweet story, lyrical language, and lovely illustrations. My children were in awe of the special fold-out spread for the big reveal of the Solstice tree. Winter: A Solstice Story is a wonderful picture book, highly recommended.
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Reviewed in the United States on October 26, 2023