query: Prove that any Hermitian Matrix is a real linear combination of Pauli operators
positive_passages.docid: 13160
positive_passages.text: Can arbitrary matrices be decomposed using the Pauli basis?
negative_passages.docid: 158724
negative_passages.text: Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
negative_passages.docid: 26801
negative_passages.text: Show that orthogonal matrices are diagonalizable
negative_passages.docid: 131906
negative_passages.text: "An operator is hermitian". Implications?
negative_passages.docid: 137209
negative_passages.text: Finding the Matrix of a Linear Operator Satisfying a Polynomial
negative_passages.docid: 30569
negative_passages.text: Prove that the only operator on $\mathbb{C}$ for which his inner product is zero is zero
negative_passages.docid: 121802
negative_passages.text: Prove that every self-adjoint unitary linear operator can be expressed in the form $U\alpha = \beta - \gamma$
negative_passages.docid: 4917
negative_passages.text: Inverse of this $3\times 3$ matrix using the Cayley–Hamilton theorem
negative_passages.docid: 29408
negative_passages.text: Get Eigensystem to return orthogonal eigenvectors for Hermitian matrix
negative_passages.docid: 35801
negative_passages.text: Traceless matrices and commutators
negative_passages.docid: 75855
negative_passages.text: Show that $\det{(A + sxy^*)}$ is linear in $s$
negative_passages.docid: 99942
negative_passages.text: A normal, idempotent linear operator must be self-adjoint
negative_passages.docid: 18012
negative_passages.text: Eigenvectors of real symmetric matrices are orthogonal
negative_passages.docid: 93550
negative_passages.text: How to find the matrix representation of an operator from its action on a basis?
negative_passages.docid: 30268
negative_passages.text: Positive definite matrix must be Hermitian
negative_passages.docid: 14550
negative_passages.text: Every Hilbert space has an orthonomal basis - using Zorn's Lemma
negative_passages.docid: 108012
negative_passages.text: A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$