Titlebook: Linear Algebra; Larry Smith Textbook 1998Latest edition Springer Science+Business Media New York 1998 Eigenvalue.Eigenvector.Lineare Algeb

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Vectors in the Plane and in Space,rawing an arrow with the magnitude and direction of the quantity in question. Physicists refer to the arrow as a ., and call the quantity so represented a .. In the study of the calculus the student has no doubt also encountered what are called vectors, particularly in connection with the study of l

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Inner Product Spaces,n important role in our intuition for the vector algebra of ℝ.and ℝ.. In fact, the length of a vector and the angle between two vectors play very important parts in the further development of linear algebra, and it is now appropriate to introduce these ingredients into our study. There are many ways

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The Spectral Theorem and Quadratic Forms,a particular form. We have not asked the related question what are the properties of those transformations whose matrices are . to have a particularly simple form. There is, in fact, a good reason for this, and it is tied up with our work of the last chapter. For example we might propose to study th

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Jordan Canonical Form,trix representative of a linear transformation. In the preceding chapter we treated this problem for self-adjoint linear transformations in a finite-dimensional inner product space. For a finite-dimensional inner product space . and a self-adjoint linear transformation.we saw that we could always fi

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Application to Differential Equations,pplications of mathematics to the physical sciences and technology. Often the equations relevant to practical applications are so difficult to solve explicitly that they can only be handled with approximation techniques on large computer systems. In this chapter we will be concerned with a simple fo

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The Similarity Problem,e apparent that there is no simple method for finding the Jordan form. By contrast, finding the diagonal form of a symmetric matrix reduces to factoring the characteristic polynomial.. Why is this? Why is the Jordan form so much more difficult to find than the diagonal or row echelon form? The reaso

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