- #1
Bill Thompson
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I am trying to solve the following problem:
Let A be a real mxn matrix. Describe the set of all vectors in F^m orthogonal to Col(A).
Here, F^m could be C^m. Now in the real case, I'd say that the column space of A is the row space of A^T, and it is well known that the row space of a matrix is orthogonal to it's null space ---> Col(a) is orthogonal to Null(A^T) (left nullspace). After significant research, I can't see how to change/adapt this statement for the complex field. Any help is greatly appreciated.
Thanks
Let A be a real mxn matrix. Describe the set of all vectors in F^m orthogonal to Col(A).
Here, F^m could be C^m. Now in the real case, I'd say that the column space of A is the row space of A^T, and it is well known that the row space of a matrix is orthogonal to it's null space ---> Col(a) is orthogonal to Null(A^T) (left nullspace). After significant research, I can't see how to change/adapt this statement for the complex field. Any help is greatly appreciated.
Thanks