query: What is happening in equation $det(A - \lambda I) = 0$ in basic terms?
positive_passages.docid: 21885
positive_passages.text: Why is the determinant useful when finding eigenvectors?
negative_passages.docid: 87425
negative_passages.text: Prove that if $A$ is a square matrix with integer entries and $\det(A) = \pm 1$, then $A^{-1}$ contains all integer entries.
negative_passages.docid: 101926
negative_passages.text: If $Q$ is a proper orthogonal transformation matrix, deduce that $\det(1-Q)=0$.
negative_passages.docid: 84341
negative_passages.text: Can the determinant of a matrix can be made $0$?
negative_passages.docid: 121767
negative_passages.text: Why $\det(A^{-1}) = 1/\det(A)$?
negative_passages.docid: 94627
negative_passages.text: What's wrong with this derivation that $i\hbar = 0$?
negative_passages.docid: 71442
negative_passages.text: How to prove $\det(I+uv^\intercal)=1+v^\intercal u$
negative_passages.docid: 125030
negative_passages.text: Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
negative_passages.docid: 47829
negative_passages.text: Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
negative_passages.docid: 103061
negative_passages.text: Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
negative_passages.docid: 113518
negative_passages.text: Determinant of the inverse matrix
negative_passages.docid: 48573
negative_passages.text: The determinant function is the only one satisfying the conditions
negative_passages.docid: 133756
negative_passages.text: Geometric interpretation of $\det(A^T) = \det(A)$
negative_passages.docid: 24072
negative_passages.text: Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
negative_passages.docid: 35155
negative_passages.text: To prove Cayley-Hamilton theorem, why can't we substitute $A$ for $\lambda$ in $p(\lambda) = \det(\lambda I - A)$?
negative_passages.docid: 50732
negative_passages.text: How to determine direct solution of determinant?
negative_passages.docid: 2271
negative_passages.text: Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix