Let V be a finite dimensional vector space, T a linear operator on V, and W a T-invariant subspa

Name: Let V be a finite dimensional vector space, T a linear operator on V, and W a T-invariant subspace of V. Denote by TW the restriction of T to W. Show that the characteristic polynomial of TW divides the characteristic polynomial of T. (Hint: start with a basis of W, complete it to a basis ? of V and study the form of the matrix [T]? of T with respect to ?.)
Uploaded: 2023-06-17T00:43:39-08:00
Duration: 3 min 22 s
Channel: Adi S
Description: Let V be a finite dimensional vector space, T a linear operator on V, and W a T-invariant subspace of V. Denote by TW the restriction of T to W. Show that the characteristic polynomial of TW divides the characteristic polynomial of T. (Hint: start with a basis of W, complete it to a basis ? of V and study the form of the matrix [T]? of T with respect to ?.)

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Sam Stansfield · Accepted Answer

1. Let $V$ be a finite-dimensional vector space and $W$ be a $T$-invariant subspace of $V$. This

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