This definition makes sense, since this determinant is independent of the choice of the basis. PM for more details. I can now talk fluently about the machinery behind least-squares problems, neural networks, etc.
This results from the fact that the determinant of a product of matrices is the product of the determinants, and thus that a matrix is invertible if and only if its determinant is invertible.
The attraction comes, I think, partly from the beauty of the subject, but also partly from the clean way in which Strang packages all of his mathematical expositions. If V has a basis of n elements, such an endomorphism is represented by a square matrix of size n.
As a programmer, this book has opened up new opportunities for me. Give this book a try—it will change your mind!
Linear algebra as portrayed by this book is a really beautiful field—much cleaner and often more intuitive than other areas at the same level calculus, differential equations, etc. Determinant The determinant of a square matrix is a polynomial function of the entries of the matrix, such that the matrix is invertible if and only if the determinant is not zero.
Strang masterfully draws the reader in and invests you into the lives of the characters.
Is the matrix invertible? The most important point, of course, is that I think you should read this book. I love this book. I spent many a nerdy weekend morning with this book and the OCW lectures.
If the dimension of V is finite, and a basis has been chosen, f and v may be represented, respectively, by a square matrix M and a column matrix and z; the equation defining eigenvectors and eigenvalues becomes M.
The determinant of an endomorphism is the determinant of the matrix representing the endomorphism in terms of some ordered basis. Strang also demonstrates why he is internationally known as a master of the thriller genre. These follow the book very closely and are indispensable—Strang is an even better lecturer than he is a writer.
I can understand these gripes, and this is why the lectures are really absolutely necessary until one has adjusted to the writing style. Will Professor Xu curve the class??vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. Another standard is book’s audience: sophomores or juniors, usually with a background of at least one semester of calculus.
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Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides/5(2). The book is designed to be a supplement for learning linear algebra by problem solving, so it may not have the focus you're looking for.
share | cite | improve this answer edited Feb 11 '10 at LINEAR ALGEBRA James B. Carrell [email protected] (July, ) 2. Contents 1 Introduction 11 This book is directed more at the former audience linear algebra: matrices, linear systems, Gaussian elimination, inverses of matrices and the LDU decomposition.
In this material, we manage to deﬁne. This book is the first part of a three-part series titled Problems, Theory and Solutions in Linear Algebra. This first part contains over solved problems and exercises.
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