Transcription of Eigenvalues, eigenvectors, and eigenspaces of linear ...
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Eigenvalues, eigenvectors , andeigenspaces of linear operatorsMath 130 linear AlgebraD Joyce, Fall 2015 Eigenvalues and re lookingat linear operators on a vector spaceV, that is, linear transformationsx7 T(x) from the vectorspaceVto finite dimensionnwith a specifiedbasis , thenTis described by a squaren nmatrixA= [T] .We re particularly interested in the study the ge-ometry of these transformations in a way that wecan t when the transformation goes from one vec-tor space to a different vector space, namely, we llcompare the original vectorxto its imageT(x).Some of these vectors will be sent to other vectorson the same line, that is, a vectorxwill be sent toa scalar multiple xof a given linear operatorT:V V, a nonzero vectorxand a constant scalar arecalled aneigenvectorand itseigenvalue, respec-tively, whenT(x) = x.
Eigenvalues, eigenvectors, and eigenspaces of linear operators Math 130 Linear Algebra D Joyce, Fall 2015 Eigenvalues and eigenvectors. We’re looking at linear operators on a vector space V, that is, linear transformations x 7!T(x) from the vector space V to itself. When V has nite dimension nwith a speci ed
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