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128
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Showing $\lambda I_V$ diagonalizable and has only one eigenvalue

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#linear-algebra #solution-verification #eigenvalues-eigenvectors #diagonalization #characteristic-polynomial
74
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Proof in infinite-dimensional space

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#linear-algebra #linear-transformations #minimal-polynomials #characteristic-polynomial #infinite-matrices
168
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If two matrices have same characteristic polynomial, then if square root for one exists, it also exists for the other one.

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#linear-algebra #characteristic-polynomial
113
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How to find the eigenvalues and their geometric multiplicities without being given a matrix

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#linear-algebra #eigenvalues-eigenvectors #determinant #characteristic-polynomial
88
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General solution for the characteristic polynomial of a matrix of $n\times n$ matrix sub-blocks

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#finite-fields #characteristic-polynomial
201
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Eigenvalues of symmetric tridiagonal matrices with complex entries

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#linear-algebra #matrices #eigenvalues-eigenvectors #characteristic-polynomial #tridiagonal-matrices
68
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How do you get the characteristic polynomial of a recursion?

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#recurrence-relations #recursion #fibonacci-numbers #characteristic-polynomial
37
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Characteristic polynomial of 4 by 4 function matrix

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#matrices #polynomials #eigenvalues-eigenvectors #determinant #characteristic-polynomial
189
Views

If $A$ commutes with $(AB - BA)^2$, is $\det(AB - BA) = 0$?

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#matrices #eigenvalues-eigenvectors #matrix-calculus #characteristic-polynomial #cayley-hamilton
48
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Why does the character of the alternating $2$-tensor representation appear in characteristic polynomial of a $3 \times 3$ matrix?

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#representation-theory #characteristic-polynomial
72
Views

Prove that A^k = 0 implies A^2 = 0 for A_2x2

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#linear-algebra #matrices #vector-spaces #eigenvalues-eigenvectors #characteristic-polynomial
88
Views

Show that characteristic polynomial of $Ty = ay$ is power of minimal polynomial of $a$

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#field-theory #galois-theory #extension-field #minimal-polynomials #characteristic-polynomial
198
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Minimal polynomial and characteristic polynomial of $T$

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#linear-algebra #linear-transformations #minimal-polynomials #characteristic-polynomial
50
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How is the matrix $(sI - A)$ called whose determinant is the characteristic polynomial of a (real valued) matrix $A$?

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#linear-algebra #eigenvalues-eigenvectors #terminology #characteristic-polynomial
160
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Range Space and Null Space of Projection Matrix

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#linear-algebra #eigenvalues-eigenvectors #minimal-polynomials #characteristic-polynomial

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