Complex Eigenvalues, Eigenvectors, Vector Spaces, Inner Product - Linear Algebra

1 month ago
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Science Education linear algebra vector spaces inner product vector space eigenvalues and eigenvectors complex vector space complex inner product space dot product of complex vectors complex inner product

This video explains complex eigenvalues and eigenvectors of a real matrix, including how to obtain the general solution, meaning or what it is, formula, geometric interpretation, example practice problems. You will understand how to extend the general solution to 3x3, how to find the eigenvectors if the eigenvalues are complex, and if the matrix is diagonalizable. Complex numbers and vector spaces are also covered.

0:00 Revision on complex numbers
5:48 Complex eigenvalues
7:30 Complex vector spaces
11:26 Complex matrices
14:04 Complex inner product
22:34 Complex eigenvalues and eigenvectors
31:12 Geometric interpretation

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