Aug 4, 2020 · The characteristic polynomial of your matrix is given by \begin {align} \chi (t) &= t^4 + 2t^3 (a + e) +t^2 (a^2 + 4ae - 2bef + d^2 + e^2) + {}\\ &\qquad+2t (a^2e - abef + ad^2 + ae^2 - be^2f - …

May 15, 2025 · In a cyclic quadrilateral ABCD inscribed in O. AC and BD are diagonals. A circle is drawn such that is is centred on the midpoint of AC, I, which is also the incenter ...

Jan 28, 2018 · The inverse of $ (X^TX)^ {-1}$ is of course $X^TX$. I suspect that's not what you actually meant, though.

Mar 28, 2018 · From here $2X^T (Xw - y) = 0$ we simply cancel out the factor $2$ and obtain the result.

We know that the Mandelbrot set is derived from the iterations of z^2 + c. Do anyone know something about magnet Mandelbrot? I found it in the software UltraFractal, and it is much more beautiful ...

Feb 26, 2017 · i think norm of any vector is always a positive real number so it is constant and derivative of constant function is zero.

May 8, 2025 · Problem: In scalene triangle $ABC$, let $K$ be the intersection of the angle bisector of $∠A$ and the perpendicular bisector of $BC$. Prove that the points $A, B, C ...

Apr 13, 2017 · Without loss of generality you can choose your coordinate system in such a way that the incircle becomes the unit circle, and none of the tangents touches it at $ (-1,0)$. In that case you can …

Feb 2, 2022 · I am preparing for Mathematical Olympiads. I recently stumbled across this Trigonometry Problem and I am unable to solve this after numerous attempts. I couldn't even find solution to it …

Feb 20, 2019 · if triangle ABC has incenter I how is it possible to show the circumcenter of triangle BIC lies on the circumcircle of triangle ABC? [![ddiagram][1]][1] D is the circumcenter of BIC