query: Let $A$ be a square matrix that commutes with its transpose. Show that the nullspaces of $A$ and $A^T$ coincide.
positive_passages.docid: 23580
positive_passages.text: Range of A and null space of the transpose of A
negative_passages.docid: 106097
negative_passages.text: Spectrum of the sum of two commuting matrices
negative_passages.docid: 49977
negative_passages.text: Show that the collection of matrices which commute with every idempotent matrix are the scalar matrices
negative_passages.docid: 122580
negative_passages.text: If N is elementary nilpotent matrix, show that N Transpose is similar to N
negative_passages.docid: 55377
negative_passages.text: Non-zero eigenvalues of $AA^T$ and $A^TA$
negative_passages.docid: 23095
negative_passages.text: Prove that T is a linear transformation
negative_passages.docid: 36090
negative_passages.text: $TT^*=T^2$, show that $T$ is self-adjoint
negative_passages.docid: 18939
negative_passages.text: Eigenvalues of the transpose
negative_passages.docid: 23372
negative_passages.text: Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set
negative_passages.docid: 131611
negative_passages.text: $A^TA$ is always a symmetric matrix?
negative_passages.docid: 156438
negative_passages.text: Find a matrix equation equivalent to $A^TPA+P=I$
negative_passages.docid: 25357
negative_passages.text: Matrices $B$ that commute with every matrix commuting with $A$
negative_passages.docid: 100549
negative_passages.text: If $e^A$ and $e^B$ commute, do $A$ and $B$ commute?
negative_passages.docid: 30996
negative_passages.text: If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint
negative_passages.docid: 59804
negative_passages.text: Show that the plane $\{su+tv|s,t \in\Bbb R\}$ in $\Bbb R^3$ is equal to the null space of some element of $(\Bbb R^3)^{*}$.
negative_passages.docid: 67990
negative_passages.text: Commutativity of matrix and its transpose
negative_passages.docid: 101861
negative_passages.text: How do you prove that $tr(B^{T} A )$ is a inner product?