Titlebook: Linear Algebra Through Geometry; Thomas Banchoff,John Wermer Textbook 1992Latest edition Springer-Verlag New York, Inc. 1992 Eigenvalue.Li

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The Geometry of Vectors in the Plane,ms which are usually expressed in the language of analytic or coordinate geometry, because vector notation enables us to use a single symbol to refer to a pair of numbers which gives the coordinates of a point. Not only does this give us convenient notations for expressing important results, but it

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Transformations of 3-Space,e vector .(.) is called the . of . under ., and the collection of all vectors which are images of vectors under the transformation . is called the . of .. We denote transformations by capital letters, such as ., etc.

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Eigenvalues,d if . is a vector perpendicular to π, then .(.) = ?.. Thus for . = 1 and . = ?1, there exist nonzero vectors . satisfying .(.) = .. If . is any vector which is neither on π nor perpendicular to π, then .(.) is not a multiple of ..

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Classification of Quadric Surfaces,ond degree; for example,.The general form of the equation of a quadric surface is. where the coefficients ., and . are constants. We would like to predict the shape of the quadric surface in terms of the coefficients, much in the same way that we described a conic section in terms of the coefficient

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,Vector Geometry in ,-Space, , ≥ 4,dimensions. What begins as an alternative way of treating problems in analytic geometry becomes a powerful tool for investigating increasingly complicated phenomena, such as eigenvectors or quadratic forms, which would be difficult to approach otherwise.

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Textbook 1992Latest edition 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 o

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Constitution

0172-6056 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 s

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