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Finding eigenvalues and eigenvectors
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Classroom Contents
Applications of Row Reduction - Gaussian Elimination I - Wild Linear Algebra A - NJ Wildberger
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- 1 CONTENT SUMMARY: pg 1: @ 3 main problems of Linear Algebra;
- 2 pg 2: @ Inverting a linear change of coordinates; example;
- 3 pg 3: @ example finished; new idea: introduce a y-sub-i matrix; to obtain the inverse of a matrix;
- 4 pg 4: @ Theorem concerning an invertible matrix;
- 5 pg 5: @ Finding eigenvalues and eigenvectors of an nXn matrix; remark about the Homogeneous case;
- 6 g 6: @14:23 The eigenvalue problem using row reduction; example1; check of result @;
- 7 pg 7: @ example2 as a reminder of the physical meaning of an eigenvector equation see WildLinAlg7;
- 8 pg 8: @ example2 continued; finding the eigenvectors using row reduction; perpendicular eigenvectors;
- 9 pg 9: @27:52 How to calculate a determinant; characteristics of a determinant; as the volume of a parallelpiped; properties of a determinant necessary to do row reduction @;
- 10 pg 10: @ the determinant of an upper triangular matrix;
- 11 pg 11: @35:11 example: putting a matrix in upper triangular form to obtain its determinant; remark about this lesson @ ;
- 12 pg 12: @ exercises 15.1:2 ; invert some systems using row reduction; find inverse matrices;
- 13 pg 13: @ exercises 15.3:4 ; find eigenvalues and eigenvectors; compute determinants; THANKS to EmptySpaceEnterprise
- 14 Introduction
- 15 Inverting a linear change of co - ods
- 16 Inverting a square invertible matrix by row reduction
- 17 Finding eigenvalues and eigenvectors
- 18 The eigenvalue problem using row reduction
- 19 How to calculate a determinant
- 20 If A is upper triangular then detA= product of diagonal entries
- 21 Exercises: invert some systems using row reduction; find inverse matrices
- 22 exercises 15.3:4 ; find eigenvalues and eigenvectors; compute determinants
