Orthogonality and Kernel Relationship Determination

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Let B be a matrix. How can I tell which (img(B), ker(B^T), img(B^T)) spaces are necessarily orthogonal to ker(B) under standard dot product?



I know the image represents the column space, but I don't understand how we can relate that to determining orthogonality to the Kernel. What characteristic of a matrix shows orthogonality to the kernel?




linear-algebra linear-transformations orthogonality




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  • How is this substantially different from your previous question?
    – amd
    2 days ago










  • no one responded. So I have to ask the question again before it gets buried
    – seekingalpha23
    2 days ago














up vote
0
down vote

favorite












Let B be a matrix. How can I tell which (img(B), ker(B^T), img(B^T)) spaces are necessarily orthogonal to ker(B) under standard dot product?



I know the image represents the column space, but I don't understand how we can relate that to determining orthogonality to the Kernel. What characteristic of a matrix shows orthogonality to the kernel?




linear-algebra linear-transformations orthogonality




share|cite|improve this question



















  • How is this substantially different from your previous question?
    – amd
    2 days ago










  • no one responded. So I have to ask the question again before it gets buried
    – seekingalpha23
    2 days ago












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Let B be a matrix. How can I tell which (img(B), ker(B^T), img(B^T)) spaces are necessarily orthogonal to ker(B) under standard dot product?



I know the image represents the column space, but I don't understand how we can relate that to determining orthogonality to the Kernel. What characteristic of a matrix shows orthogonality to the kernel?




linear-algebra linear-transformations orthogonality




share|cite|improve this question











Let B be a matrix. How can I tell which (img(B), ker(B^T), img(B^T)) spaces are necessarily orthogonal to ker(B) under standard dot product?



I know the image represents the column space, but I don't understand how we can relate that to determining orthogonality to the Kernel. What characteristic of a matrix shows orthogonality to the kernel?





linear-algebra linear-transformations orthogonality





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked 2 days ago









seekingalpha23

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  • How is this substantially different from your previous question?
    – amd
    2 days ago










  • no one responded. So I have to ask the question again before it gets buried
    – seekingalpha23
    2 days ago
















  • How is this substantially different from your previous question?
    – amd
    2 days ago










  • no one responded. So I have to ask the question again before it gets buried
    – seekingalpha23
    2 days ago















How is this substantially different from your previous question?
– amd
2 days ago




How is this substantially different from your previous question?
– amd
2 days ago












no one responded. So I have to ask the question again before it gets buried
– seekingalpha23
2 days ago




no one responded. So I have to ask the question again before it gets buried
– seekingalpha23
2 days ago















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