Inner product and orthogonality in non orthogonal basis
According to the definition of orthogonality (on finite vector spaces), Given an inner product space, two vectors are orthogonal if their inner product is...
Apr 16, 2026 1 VIEWS
Topic: General
5104 Articles 
How to find a Solution of this $(3x + y - z)p + (x + y - z)q = 2(z -y)$ linear PDE of first order?
The given equation is $$(3x + y - z)p + (x + y - z)q = 2(z -y)$$ where $$p = \frac{\partial z}{\partial x}, q = \frac{\partial z}{\partial y}$$ In my text...
Apr 16, 2026 1 VIEWS
proof of perpendicular lines in a circle
$AB$ is a chord of a circle, centre $O$, and $M$ is its midpoint . The radius from $O$ is drawn through the midpoint $M$. Prove that $OM$ is perpendicular...
Apr 16, 2026 1 VIEWS
Definition of osculating plane
I couldn't understand the exact geometrical meaning of the osculating plane definition. Can any one help me with this? Thanks advance. Osculating pla...
Apr 16, 2026 1 VIEWS
Krull dimension of polynomial rings over noetherian rings
I want to prove the following theorem concerning Krull dimension: Theorem If $A$ is a noetherian ring then $$\dim(A[x_1,x_2, \dots , x_n]) = \dim(A) + n$$...
Apr 16, 2026 1 VIEWS
The 2nd derivative of $x^2+y^2=4$
Finding the first derivative of the function $x^2+y^2=4$ gives you $$y'=-\frac{x}{y} $$ Then to find the 2nd derivative you apply the quotient rule, ...
Apr 16, 2026 1 VIEWS
How do you draw a DFA from a regular expression?
I want to draw a DFA from the below language: The set of strings in $\{a, b\}$ where every $a$ is immediately followed by $b$ I can write the regular expr...
Apr 16, 2026 1 VIEWS
Need References That Discuss The Mathematical Number Known as Wau
For those not familiar, perhaps this link in which Vi Hart discusses the number will be useful: http://www.youtube.com/watch?v=GFLkou8NvJo However, I cann...
Apr 16, 2026 1 VIEWS
Fourier transform of the characteristic function
My qustion is about the Fourier transform of the characteristic function $\chi_{[0,1]}$. How can I find what it is? The problem is I got something really ...
Apr 16, 2026 2 VIEWS
How to define a sphere inversion transformation in 3D?
I would like to define a circle inversion like transformation for a sphere? I saw inversion in higher dimensions on wiki, but it doesn't elaborate mu...
Apr 16, 2026 1 VIEWS
Find the complementary solution of the following differential equation.
I need to find the general solution of the following differential equation: $$ y''' - y'' - y' + y = 4e^{-t} + 3 $$ My solut...
Apr 16, 2026 1 VIEWS
X = a/ (1+a) . Would the value of x increase or decrease if “a” increases?
It’s pretty easy to find the answer after putting in random values but I can’t wrap my head around with my below explanation which is in direct contradict...
Apr 16, 2026 1 VIEWS