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Mitur
Mitur asked in Science & MathematicsMathematics · 1 decade ago

Why is the dimension of column space = dimension of row space = rank?

Hi, from linear transformation, I understand the rank is the dimension of the set of vectors after the transformation takes place.

Hence, looking at a matrix as a transformation, the dimension of column space = rank.

But why is the dimension of row space = rank also? What is the relationship between row space and column space?

Thanks.

1 Answer

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  • lmlm
    Lv 6
    1 decade ago
    Favorite Answer

    rank(A) = rank(A')

    where ' denotes transpose.

    Now the rows of A are columns of A', and think of it in the way that you understand it.

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