Consider a mapping $F: \mathbf{R}^n \rightarrow \mathbf{R}^3 (n \geqslant 3)$ defined by an ordered triple of real-valued quadratic forms; if some linear combination ...

\(y = x + 3\) is a linear equation and \(y = x^2 + 3x\) is a quadratic equation. If the product of two numbers is zero, then one or both numbers must also be equal to zero. To solve, put each bracket ...

For the Gaussian sequence model, we obtain nonasymptotic minimax rates of estimation of the linear, quadratic and the ℓ2-norm functionals on classes of sparse vectors and construct optimal estimators ...

Simultaneous equations Simultaneous examples with no common coefficients Creating and solving simultaneous equations Simultaneous equations with linear and quadratic Solving simultaneous equations ...