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ZixuanZhang
ZixuanZhang
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Similar matrices

for some invertible ; similar matrices represent the same linear map and share trace, determinant, and characteristic polynomial.

Definition 4.14

We say that two matrices and of size are similar if

for some invertible matrix .

Invariants under similarity

If , then

so similar matrices represent the same linear map with respect to different bases.

For the particular case , this means a diagonalisable matrix satisfies

Related

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