The discussion centers on the relationship between the null space of a matrix A and its transposed matrix, denoted as transpose(A). It is established that if matrix A has dimensions m x n (with m < n) and its rank is less than m, then the null space of transpose(A) exists. The participants inquire whether null(transpose(A)) can be derived from null(A) or if it necessitates a separate computation. The consensus indicates that while there is a relationship, the null space of the transposed matrix must generally be computed independently.
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Patlam81 said:Let says I have a matrix A with m rows and n columns, with m<n, from which I compute the null space. If the rank of A is smaller than m, then the null space of the transpose of A also exists. Is there any relation between the null space of a matrix and the null space of the transposed matrix? Can I find null(transpose(A)) from null(A) or I have to compute the nullspace again?