Matrice u visokoškolskoj matematici nezaobilazni su dio sadržaja kojeg studenti moraju savladati. Shvaćanje pojma matrica ne predstavlja velik problem za studente kao ni operacije transponiranja, ...zbrajanja i oduzimanja. Problemi nastaju kod množenja, traženja inverza i rješavanja sustava linearnih jednadžbi primjenom Gaussove metode transformacija. Matrix Reshish je mrežna stranica koja je prilagođena za korištenje putem mobilnih uređaja, a sadrži matrični kalkulator. Kalkulator je koncipiran tako da daje rješenje postavljenog zadatka korak po korak, što uvelike olakšava studentu uvježbavanje rješavanja zadatka.
Pojam svojstvenih vrijednosti i spektra matrice odavno se istražuje i koristi u matematici. Svojstvene vrijednosti matrica u mnogim slučajevima daju izvrstan uvid u svojstva samih matrica, no katkada ...ne daju dovoljno informacija za rješavanje problema na koje se može naići. Takvi se slučajevi pojavljuju u raznim granama matematike kao npr. teorije operatora i teorije Markovljevih lanaca i ostalih znanosti, od populacijske ekologije, preko laserske tehnologije, kvantne mehanike i hidrodinamike.
Katkada se preciznije informacije o matrici mogu dobiti korištenjem pseudospektra te je cilj ovog članka dati čitatelju osnovne informacije o ovom zanimljivom poopćenju pojma spektra.
U ovom će članku biti navedeni osnovni pojmovi vezani uz pseudospektar, ekvivalentne definicije pseudospektra, odnos prema običnom spektru matrica, kao i neka osnovna svojstva.
http://e.math.hr/math_e_article/br18/nakic_petric
This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a ...one-semester course, "Applied Linear Algebra and Matrix Analysis" places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. The student will develop a solid foundation in the following topics: Gaussian elimination and other operations with matrices; basic properties of matrix and determinant algebra; standard Euclidean spaces, both real and complex; geometrical aspects of vectors, such as norm, dot product, and angle; eigenvalues, eigenvectors, and discrete dynamical systems; and, general norm and inner-product concepts for abstract vector spaces.; For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable. Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory.
This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, ...linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with important applications.
The second edition contains two new chapters: a chapter on convexity, separation and positive solutions to linear systems and a chapter on the QR decomposition, singular values and pseudoinverses. The treatments of tensor products and the umbral calculus have been greatly expanded and there is now a discussion of determinants (in the chapter on tensor products), the complexification of a real vector space, Schur's lemma and Gersgorin disks.
Basic Linear Algebra is a text for first year students, working from concrete examples towards abstract theorems, via tutorial-type exercises. The book explains the algebra of matrices with ...applications to analytic geometry, systems of linear equations, difference equations, and complex numbers. Linear equations are treated via Hermite normal forms, which provides a successful and concrete explanation of the notion of linear independence. Another highlight is the connection between linear mappings and matrices, leading to the change of basis theorem which opens the door to the notion of similarity. The authors are well known algebraists with considerable experience of teaching introductory courses on linear algebra to students at St Andrews. This book is based on one previously published by Chapman and Hall, but it has been extensively updated to include further explanatory text and fully worked solutions to the exercises that all 1st year students should be able to answer.
