- #1

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^{T}=-A.

1). Prove u

^{T}Au=0 for every u in R. (I made it)

2). Prove I

_{n}+ A is a invertible matrix.

I have no idea how to prove the 2nd.

Thanks

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- Thread starter weasel3000
- Start date

- #1

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1). Prove u

2). Prove I

I have no idea how to prove the 2nd.

Thanks

- #2

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Anyway, I'll give a hint. For which vectors u, does (I+A)u=0. Use (1) for this.

- #3

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Anyway, I'll give a hint. For which vectors u, does (I+A)u=0. Use (1) for this.

??? not get it. 0*u=0; (I+A)*0=0; non-zero vector *non-zero vector=0 also possible.

- #4

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You're right, if u=0, then (I+A)u=0. Are there other possibilities for u?

- #5

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- #6

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- #7

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oh my god. i am gonna find a place to cry. i just know the null space. never learn what kernel and injective operators are. Thank you again. I am gonna learn that damn THINGS tonight.

- #8

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