query: For any real matrix $M$ let, $\lambda^{+}(M)$ be the number of positive eigenvalues of $M$ counting multiplicities.
positive_passages.docid: 28122
positive_passages.text: For any real square matrix which are correct?
negative_passages.docid: 156834
negative_passages.text: Why are there $736$ matrices $M\in \mathcal M_2(\mathbb{Z}_{26})$ for which it holds that $M=M^{-1}$?
negative_passages.docid: 19132
negative_passages.text: Similar matrices have the same eigenvalues with the same geometric multiplicity
negative_passages.docid: 155082
negative_passages.text: If $P$ is real orthogonal matrix with $\det P = -1$, prove that $-1$ is an eigenvalue of $P$.
negative_passages.docid: 27865
negative_passages.text: What is the number of invertible $n\times n$ matrices in $\operatorname{GL}_n(F)$?
negative_passages.docid: 68132
negative_passages.text: Small positive eigenvalues found for a negative definite matrix
negative_passages.docid: 51834
negative_passages.text: Positivity of a determinant
negative_passages.docid: 41813
negative_passages.text: How to prove positive (semi-)definitness in matrix notation without numbers
negative_passages.docid: 31326
negative_passages.text: Number of $(0,1)$ $m\times n$ matrices with no empty rows or columns
negative_passages.docid: 98656
negative_passages.text: Geometric multiplicity of the largest eigenvalue
negative_passages.docid: 125569
negative_passages.text: Prove that the eigenvalues of a real symmetric matrix are real
negative_passages.docid: 24454
negative_passages.text: The relationship between the eigenvalues of matrices $XY$ and $YX$
negative_passages.docid: 98323
negative_passages.text: If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
negative_passages.docid: 1973
negative_passages.text: Traces of all positive powers of a matrix are zero implies it is nilpotent
negative_passages.docid: 39993
negative_passages.text: Count the number of positive solutions for a linear diophantine equation
negative_passages.docid: 100731
negative_passages.text: Positive operator has a positive spectrum?
negative_passages.docid: 55377
negative_passages.text: Non-zero eigenvalues of $AA^T$ and $A^TA$