Linear Algebra Through GeometrySpringer Science & Business Media, 10. sep. 1993 - 308 strani 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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2bxy 3-space a₁ a₂ ax² axis b₁ b₂ b3 b₁x₁ C₁ calculate Chapter 3.0 characteristic equation column coordinate axes define denote det(m determinant diagonal matrix dimensions dot product E₁ E₂ eigenvalues eigenvector corresponding eigenvectors elementary matrices EXAMPLE Exercise 11 Figure Find all solutions formula function G₁ geometry Hence homogeneous system inner product inverse isometry length linear algebra linear transformation linearly independent n-tuple nonzero vector obtained origin orthogonal matrix orthonormal basis parallelogram perpendicular plane polynomial positively oriented preserves orientation projection PROOF Proposition radians real number rotation scalar multiple set of vectors Show Similarly solve Spectral Theorem subspace symmetric matrix t₁ t₂ Theorem transformation of R3 transformation with matrix triplet u₁ unit vector vector space x-axis X₁ Y₁ zero а2 аз