Show that $(9-5\sqrt 3)(2-\sqrt 2) $ is not a square in $\mathbb Q (\sqrt 2, \sqrt 3) $; equivalently, prove that $\mathbb Q (\sqrt 2, \sqrt 3, u)$ is of ...

In Kreyszig's Functional Analysis, page no. 303, exercise no. 3 says that completeness cannot be omitted from Banach's Fixed Point Theorem. But ...

I want to factor this polynomial without using the quadratic formula. So, as the first step I multiply coefficient of $x^2$ with $-10$. The product obtain...

I am trying to find the center and radius of the circle with equation $x^2 + y^2 -6x + 10y + 9 = 0$

Stuck on this question: Let $$A=\begin{pmatrix} 2&1\\ -1&-1 \end{pmatrix}$$$$B=\begin{pmatrix} -2&5\\ -1&3 \end{pmatrix}$$$$C=\begin{pmatr...

Given $\nabla \cdot u = 0$ and $w = \nabla \times u$ equation 9 of http://projecteuclid.org/euclid.cmp/1103941230 has the identity $u = - \nabla \times (\...

I'm a little confused as to some linear algebra notation and would appreciate some clarification. There exists an $n\times n$ diagonal matrix $Q$ whe...

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I am trying to figure out how to input product notation into my TI-84 Plus graphing calculator. I haven't found anything so far. Is there any functio...

If i have $\sum_{n=1}^\infty a_n=A$ and $\sum_{n=1}^\infty b_n=B$, can i write $\sum_{n=1}^\infty a_n\cdot b_n$ in function of $A$ and $B$ ?