Idempotent Matrices and Invertibility Problems
We discuss properties of idempotent matrices. These are matrices, P, for which we have P^2 = P. Natural examples of these type of operators are projections. ...
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About this video
We discuss properties of idempotent matrices. These are matrices, P, for which we have P^2 = P. Natural examples of these type of operators are projections. Aside from the identity, these matrices are never invertible. We discuss how perturbations of the identity by an idempotent matrix do have nice invertibility properties.
#mikethemathematician, #mikedabkowski, #profdabkowski
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286
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11
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Duration
8:27
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Published
Jul 10, 2024
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hd
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#mike the mathematician #mike dabkowski math #Linear Algebra #Matrix Algebra #Matrix Operations #Linear Algebra Solutions #Matrix Algebra Solutions #idempotent matrices #the only invertible idempotent matrix is the identity #eigenvalues of idempotent matrices #idempotency #idempotency of matrix #class of idempotent matrices #I-aP invertible #perturbations of the identity by an idempotent matrix
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