query: Linear Algebra Problem - columns of $A$ are linearly independent $\Rightarrow$ $A^TA$ non-singular
positive_passages.docid: 131701
positive_passages.text: Why is $A^TA$ invertible if $A$ has independent columns?
negative_passages.docid: 55031
negative_passages.text: Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
negative_passages.docid: 27248
negative_passages.text: If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$
negative_passages.docid: 145876
negative_passages.text: $AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.
negative_passages.docid: 31149
negative_passages.text: Prove that matrix can be square of matrix with real entries
negative_passages.docid: 35874
negative_passages.text: Show that when $BA = I$, the solution of $Ax=b$ is unique
negative_passages.docid: 58329
negative_passages.text: Show that $y_1$ and $y_2$ are not Linearly Independent
negative_passages.docid: 147797
negative_passages.text: If $A$ is an invertible matrix, then the column span of $A$ equals $F^{n\times1}$
negative_passages.docid: 92600
negative_passages.text: Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
negative_passages.docid: 42495
negative_passages.text: Determine if the following sets of vectors are linearly independent
negative_passages.docid: 60598
negative_passages.text: Matrix $A^T A$ as sum of outer products
negative_passages.docid: 98298
negative_passages.text: Prove that bilinear form can be presented as product of linear forms if and only if it has rank one
negative_passages.docid: 98604
negative_passages.text: Linear Algebra problem about limits
negative_passages.docid: 123665
negative_passages.text: A question in Subspaces in linear algebra
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: 152147
negative_passages.text: Why is a set of orthonormal vectors linearly independent?
negative_passages.docid: 22531
negative_passages.text: Testing for linear dependence among the columns of a matrix