query: Show that matrix $ M=\alpha^2 I +AA^T$ is nonsingular
positive_passages.docid: 141286
positive_passages.text: When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
negative_passages.docid: 112701
negative_passages.text: Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
negative_passages.docid: 130268
negative_passages.text: How to prove that a nilpotent matrix is not invertible?
negative_passages.docid: 98646
negative_passages.text: Show determinant of matrix is non-zero
negative_passages.docid: 50404
negative_passages.text: How to prove a matrix is nilpotent?
negative_passages.docid: 129977
negative_passages.text: Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
negative_passages.docid: 36771
negative_passages.text: How to prove that A is normal if and only if there's a unitary matrix V,s.t. A*=AV?
negative_passages.docid: 35345
negative_passages.text: How do i prove invertibility of this linear transformation
negative_passages.docid: 15969
negative_passages.text: How to prove that $A$ is positive semi-definite if all principal minors are non-negative?
negative_passages.docid: 110086
negative_passages.text: Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
negative_passages.docid: 19424
negative_passages.text: Showing $(M^\perp)^\perp=\overline{M}$
negative_passages.docid: 3150
negative_passages.text: Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
negative_passages.docid: 131611
negative_passages.text: $A^TA$ is always a symmetric matrix?
negative_passages.docid: 28460
negative_passages.text: Show matrix is nilpotent
negative_passages.docid: 52882
negative_passages.text: find nonsingular matrices $B$ and $C$ that satisfy $BC+ CB= 0$
negative_passages.docid: 5322
negative_passages.text: Let $A$ be a complex matrix such that $A^n = I$, show that $A$ is diagonalisable.
negative_passages.docid: 109228
negative_passages.text: Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent