query: Trace of the product of two matrices and singular values
positive_passages.docid: 38850
positive_passages.text: How to show Von Neumann Trace inequality $ \text{Tr}(AB) \leq \sum_{i=1}^n \sigma_{A,i}\sigma_{B,i} $?
negative_passages.docid: 1865
negative_passages.text: Sub-determinants of an orthogonal matrix
negative_passages.docid: 37060
negative_passages.text: The Parallelogram Identity for an inner product space
negative_passages.docid: 5058
negative_passages.text: Eigenvalues of the rank one matrix $uv^T$
negative_passages.docid: 54740
negative_passages.text: Proofs of Determinants of Block matrices
negative_passages.docid: 116376
negative_passages.text: Prove the determinant is the product of its diagonal entries
negative_passages.docid: 88746
negative_passages.text: Positive definiteness of the matrix $A+B$
negative_passages.docid: 63753
negative_passages.text: Eigenvalues of product of two complex matrices
negative_passages.docid: 31029
negative_passages.text: Characteristic polynomial of a matrix of $1$'s
negative_passages.docid: 126337
negative_passages.text: Eigenvalues in orthogonal matrices
negative_passages.docid: 39585
negative_passages.text: Connection between rank and matrix product
negative_passages.docid: 48658
negative_passages.text: Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
negative_passages.docid: 57318
negative_passages.text: Property of the conjugate transpose matrix with inner product
negative_passages.docid: 90506
negative_passages.text: Finite multiplicative group of matrices with sum of traces equal to zero.
negative_passages.docid: 65783
negative_passages.text: Proving: "The trace of an idempotent matrix equals the rank of the matrix"
negative_passages.docid: 125889
negative_passages.text: Determinant of rank-one perturbations of (invertible) matrices
negative_passages.docid: 18939
negative_passages.text: Eigenvalues of the transpose