## 3000 Solved Problems in Linear AlgebraMaster linear algebra with Schaum's--the high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! 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. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests; Study quickly and more effectively; Learn the best strategies for solving tough problems in step-by-step detail; Get the big picture without spending hours pouring over long textbooks. Review what you've learned in class by solving thousands of relevant problems that test your skill. Compatible with any classroom text, Schaum's Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to remember--fast! And Schaum's are so complete, they're perfect for preparing for graduate or professional exams. Inside you will find: 3000 solved problems with complete solutions--the largest selection of solved problems yet published on linear algebra; A superb index to help you quickly locate the types of problems you want to solve; Problems like those you'll find on your exams; Techniques for choosing the correct approach to problems; Guidance on choosing the quickest, most efficient solution. If you want top grades and thorough understanding of linear algebra, this powerful study tool is the best tutor you can have! Chapters include: Vectors in R" and C." Matrix Algebra. Systems of Linear Equations. Square Matrices.Determinants. Algebraic Structures. Vector Spaces and Subspaces. Linear Dependence, Basis, Dimension. Mappings. Linear Mappings. Spaces of Linear Mappings. Matrices and Linear Mappings. Change of Basis, Similarity. Inner Product Spaces, Orthogonality. Polynomials over a Field. Eigenvalues and Eigenvectors, Diagonalization. Canonical Forms. Linear Functionals and the Dual Space. Bilinear, Quadratic, and Hermitian Forms. Linear Operators on Inner Product Spaces. Applications to Geometry and Calculus. |

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### Contents

VECTORS IN R AND C | 1 |

MATRIX ALGEBRA | 28 |

SYSTEMS OF LINEAR EQUATIONS | 51 |

Copyright | |

17 other sections not shown

### Common terms and phrases

Accordingly algebra algorithm basis vectors belong bilinear form block matrix change-of-basis matrix characteristic polynomial characteristic polynomial A(f coefficients column vector commutative coordinate vector coset denote determinant diagonal entries diagonal matrix diagonalizable dimension echelon form eigenvalue eigenvectors equal exists field Find a formula Find the matrix form a basis free variables hence Hermitian homogeneous system identity element inner product space integers invertible linear combination linear equations linear map linear operator linearly independent matrix representation n-square matrix nilpotent nonsingular nonzero solution nonzero vector normal one-to-one orthogonal orthogonal matrix orthonormal basis permutation positive definite Problem Prove Theorem quadratic form real numbers reduce to echelon refer root row canonical form row reduce row space scalar multiplication Show Solve span square subset subspace Substitute Suppose symmetric matrix system of linear transpose unique solution unknowns upper triangular usual basis vector space Write