query: For a non-diagonalizable $n \times n$ matrix, how to prove that $\exists (A_m)$ is diagonalizable matrix such that $A_m$ converges to $A$.
positive_passages.docid: 18145
positive_passages.text: Diagonalizable matrices with complex values are dense in set of $n\times n$ complex matrices.
negative_passages.docid: 128835
negative_passages.text: Compactness of the set of $n \times n$ orthogonal matrices
negative_passages.docid: 69542
negative_passages.text: Why do the $n \times n$ non-singular matrices form an "open" set?
negative_passages.docid: 123803
negative_passages.text: If $X^n$ is a diagonal matrix with distinct eigenvalues, then is $X$ also a diagonal matrix with distinct eigenvalues?
negative_passages.docid: 117293
negative_passages.text: sufficient and necessary conditions for matrix to be diagonalize or triangular
negative_passages.docid: 64747
negative_passages.text: If $A^m=I$ then A is Diagonalizable
negative_passages.docid: 101176
negative_passages.text: Suppose that $(s_n)$ converges to s. Prove that $(s_n^2)$ converges to $s^2$
negative_passages.docid: 80544
negative_passages.text: Need verification - Prove a Hermitian matrix $(\textbf{A}^\ast = \textbf{A})$ has only real eigenvalues
negative_passages.docid: 25682
negative_passages.text: If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
negative_passages.docid: 69980
negative_passages.text: Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
negative_passages.docid: 35514
negative_passages.text: If $\{f_n\}$ converges uniformly and each $f_n$ is bounded, show that $\exists M>0$ s.t. $|f_n(x)| \leq M$
negative_passages.docid: 98631
negative_passages.text: Postive-semidefiniteness of matrix with entries $1/(a_i+a_j)$
negative_passages.docid: 111353
negative_passages.text: Show that $\{a_n\}$ defined by $a_{n+1}=\frac{a_n+2}{a_n+1}$ converges
negative_passages.docid: 135316
negative_passages.text: A basic question on diagonalizability of a matrix
negative_passages.docid: 837
negative_passages.text: Suppose that $(s_n)$ converges to $s$, $(t_n)$ converges to $t$, and $s_n \leq t_n \: \forall \: n$. Prove that $s \leq t$.
negative_passages.docid: 72541
negative_passages.text: Is the matrix diagonalizable for all values of t?
negative_passages.docid: 58339
negative_passages.text: The diagonalizable matrices are not dense in the square real matrices