query: Using a orthonormal bases of $\mathbb R^4$ and $\mathbb R^6$ find a solution $Ax=z_1$
positive_passages.docid: 151390
positive_passages.text: Let $q_1,q_2,q_3,q_4$ be orthonormal vectors in $\mathbb{R}^4$,$z_1,z_2,...,z_6$ orthonormal vectors in $\mathbb{R}^6$ and $A=z_1q_1^T + z_2q_2^T$.
negative_passages.docid: 80982
negative_passages.text: Solve $a^3+b^3+3ab=1$ with $(a,b)\in \Bbb{Z}^2$
negative_passages.docid: 131893
negative_passages.text: How to find the roots of $ x^4 + x + 1$ in the extension of $\Bbb F_2$?
negative_passages.docid: 106033
negative_passages.text: Solve the system in $\mathbb{R}$
negative_passages.docid: 53575
negative_passages.text: Describe $R=\mathbb{Z}[X]/(X^2-3,2X+4)$
negative_passages.docid: 68552
negative_passages.text: Find the representing matrix with the respect to the standard basis
negative_passages.docid: 30358
negative_passages.text: Finding Jordan basis of a matrix ($3\times3$ example)
negative_passages.docid: 154322
negative_passages.text: Localizing the zeros of $z^4+z+1$
negative_passages.docid: 128107
negative_passages.text: find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
negative_passages.docid: 32420
negative_passages.text: A complete orthonormal system contained in a dense sub-space.
negative_passages.docid: 6319
negative_passages.text: Finding an orthonormal basis for a matrix
negative_passages.docid: 125647
negative_passages.text: Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields
negative_passages.docid: 139201
negative_passages.text: Finding Jordan basis of a matrix $(4\times 4)$
negative_passages.docid: 145094
negative_passages.text: Is my basis for $U=\{p \in \mathcal P_4(\mathbb R) \mid p(6)=0\}$ correct?
negative_passages.docid: 133609
negative_passages.text: orthonormal system in a Hilbert space
negative_passages.docid: 16400
negative_passages.text: Find all solutions to the equation $(z+1)^6=z^6$. Express the solutions in simplified rectangular form. Hint: Clearly $z=0$ is not a solution.
negative_passages.docid: 112939
negative_passages.text: Find a basis for the subspace of $\mathbb{R}^4$ spanned by the given vectors.