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Product of inner products
Is product of innerproduct again a inner product of two vectors? For example - Is $ (< u,v >)(< x,y >) = < m,n > $? And if yes is m and ...
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Archimedean Principle
Prove the Archimedean principle for $\mathbb{Q}$, the set of rational numbers. I know the proof for real numbers If not, then the nonempty set $S = \{nx \...
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Convert 1-5 Grading Scale to 1-100 Grading System
I am creating a formula in Excel to convert 1-5 Grading Scale to 1-100 Grading System Suppose that I have the following table: 97-100 = 1.00 94 - 96 = 1.2...
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How do Lagrange multipliers work to find the lowest value of a function subject to a constraint?
I have been using Lagrange multipliers in constrained optimization problems, but I don't see how they actually work to simultaneously satisfy the con...
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Calculating the radius of the circumscribed sphere of an arbitrary tetrahedron, edge lengths given
In two dimensional Euclidean space, it is not hard to calculate the radius of the circumscribed circle of an arbitrary triangle when all the side lengths ...
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Proving that a transformation is an isometry and find the projectivity which reperesents
Consider the transformation: $T \begin{bmatrix} x \\ y \\ \end{bmatrix} $ $\mapsto$$\frac{\sqrt{2}}{2} \begin{bmatrix} x+y-1 \\ -x+y+1 \\ \end{bmatrix} $ ...
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How to solve a bimatrix game?
Given a bimatrix game of $$\left(\begin{matrix}(0,-1) & (0,0)\\(-90,-6)&(10, -10)\end{matrix}\right)$$ Source How to find the nash equilibrium str...
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Finding the angle between two points
First of all, I am doing some mathematical background information for a software I am creating. What I want to achieve is the point on an object rotating ...
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What does "subject to" mean in math?
For instance, I saw the expression in the Wikipedia article on Lagrange multipliers: maximize $f(x, y)$ subject to $g(x, y) = c$ What does "subject to" mean?
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Convert Degrees of Latitude to Feet
I need to check this formula I have to compute the distance of a point with latitude $lat$ from the equator: $$ \mathrm{feet} = \mathrm{lat} * 10000 \time...
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