Linear Algebra Through Geometry
Linear Algebra Through Geometry introduces the concepts of linear algebra through the careful study of two and three-dimensional Euclidean geometry. This approach makes it possible to start with vectors, linear transformations, and matrices in the context of familiar plane geometry and to move directly to topics such as dot products, determinants, eigenvalues, and quadratic forms. The later chapters deal with n-dimensional Euclidean space and other finite-dimensional vector space. Topics include systems of linear equations in n variable, inner products, symmetric matrices, and quadratic forms. The final chapter treats application of linear algebra to differential systems, least square approximations and curvature of surfaces in three spaces. The only prerequisite for reading this book (with the exception of one section on systems of differential equations) are high school geometry, algebra, and introductory trigonometry.
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Linear Algebra is the one course I regret not taking as an undergrad. This is a solid introduction that uses applications in 2D and 3D geometry to ground the potentially abstract subject. Celotno mnenje
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3-space A X B axis B X C calculate called Chapter 2.5 characteristic equation column coordinate axes coordinate axis cos0 def1ne define det(m determinant diagonal entries diagonal matrix differential system dimensions dot product eigenvalues eigenvector corresponding eigenvectors elementary matrices Example Exercise 12 express Figure Find all solutions formula function geometry given vector Hence homogeneous system hyperplane inner product inverse isometry length linear algebra linear equations linear transformation linearly independent n-tuple nonzero vector origin orthogonal matrix orthonormal basis pair of vectors parallelogram perpendicular plane polynomial positively oriented preserves orientation Proof Proposition proved radians real number reflection right-hand side rotation satisfies scalar multiple segment set of vectors Show Similarly sin0 Spectral Theorem straight line subspace Suppose symmetric matrix system H transformation of R3 transformation with matrix triplet unit vector vector in R3 vector space write x-axis zero