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## Main Question or Discussion Point

Having a matrix, how can I know if the function the matrix is representing is:

a) Injective

b) Bijective

Thanks in advance

a) Injective

b) Bijective

Thanks in advance

- Thread starter devoured_elysium
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- #1

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Having a matrix, how can I know if the function the matrix is representing is:

a) Injective

b) Bijective

Thanks in advance

a) Injective

b) Bijective

Thanks in advance

- #2

quasar987

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it is injective iff for all w in W, there is at most one v in with with L(v)=w

it is bijective if it is injective and surjective.

These are the definitions. If you're having trouble applying them to a specific problem, you should tell us what the exact problem is and what you've attempted (if anything) and then we can help more.

- #3

HallsofIvy

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In order to be "bijective" a mapping must be both injective and surjective: "one-to-one" and "onto". For a linear transformation represented by a matrix, that means it must be n by n for some positive integer n and have rank n.

- #4

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If I understood well, any matrix with non-zero determinant will be bijective, right?

I don't quite get what you mean by domain space and range space. I know what a vector space is. Is it related to it?

Thanks

- #5

quasar987

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