# Questions tagged [geometric-interpretation]

Questions about understanding a problem geometrically.

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### What is the geometric interpretation of $\frac{1}{2}||a||^2\leq \langle a,b\rangle$?

Give $a, b$ in $\mathbb{R}^n$. What is the geometric interpretation of the following? $$\frac{1}{2}\|a\|^2 \leq \langle a,b\rangle$$ In other words, what criteria should $a$ and $b$ have to satisfy ...
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### What is the geometric interpretation of matrix addition?

I was studying linear algebra and trying to get a visual "feel" for it through watching 3Blue1Brown's "Essence Of Linear Algebra" series here Essence Of Linear Algebra Here, matrix ...
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### Geometric interpretation of row operations on matrix (when solving systems of equations)

I understand that 2D matrix representing the lines in 2D space gives a unique solution where those lines intersect. Same in 3d, unique solution is where the planes intersect. Can someone explain what ...
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### Generalizing the geometric interpretation of dot product to simple $k$-vectors

Background: For $u, v \in \mathbb R^n$, the dot product $u \cdot v$ can be interpreted geometrically as follows: Its magnitude is the product of the lengths of $u$ and $\operatorname{proj}_{u} v$. ...
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### Geometric intepretation of transpose of matrix [duplicate]

Whenever we see a matrix $A=\bigl( \begin{smallmatrix} 3 & 2 \\ 1 & 2 \end{smallmatrix} \bigr)$ and $v=(3, 2),$ we can visualize that $(3, 2)$ represent the coordinates of $\mathbf i$ vector ...
1 vote
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### basic level maths to geometrical interpolations (trilinear, prism, pyramid, tetrahedral) - where do I start?

I'm attempting to read Computational Color Technology by Henry R. Kang but I only have a GCSE level understanding of maths (if even that, it was 15 years ago..). I'd like to learn about geometrical ...
1 vote
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### A question about derivatives between Euclidean spaces: how should we construct it and interpret its definition?

As it is known from the single-variable calculus, given $X\subseteq\textbf{R}$, a function $f:X\to\textbf{R}$ and a adherent point $x_{0}\in X$ which is also a limit point, we define the derivative of ...
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### How can 2 independent variables lead to a single variable parametrization? (Intuition)

Take the following formula: $$\mu_{ij}=\left(\alpha_i\Sigma_i^{-1}+\alpha_j\Sigma_j^{-1}\right)^{-1} \left(\alpha_i\Sigma_i^{-1}\mu_i+\alpha_j\Sigma_j^{-1}\mu_j\right).$$ Where the alphas are ...
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### What it is the interpretation of the below picture in set theory?

somone sent me the below picture and He asked me to give him its interpretation regarding set theory ? but I ask alos about its geometricall interpretation ?
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### Examples about Cohen-Macaulay property of rings and book recommendation on intuition

My professor asks me to give an example about a local non-CM rings that are CM after modding out at any minimal prime. After a while failing to do so, I believe it is impossible since there exists a ...
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### What does the primitive relations "betweenness" defined in Cayley–Klein model? What's the difference to the Euclidean geometry?

What does the primitive relations "betweenness" defined in Cayley–Klein model? What's the difference to the Euclidean geometry? In the link below, is $n$ between $k$ and $m$ in the Klein-Beltrami ...
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### Linear Algebra, Geometric Representation of the Span of a Set of Vectors

Given the vectors: [4, 3, 3], [0, 1, 1], and [-1, 0, 0] The question: Is the vector [4, 4, 3] in the span of the set? I believe it is NOT, since putting the augmented matrix for this set in row-...
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### What is the geometric interpretation of a separable space?

What is the geometric interpretation of a separable space? I know the definition of a separable space and I can give some examples.
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### Draw solutions to complex number inequality $0 < \arg[(1-i)\overline z ] \le \frac \pi 4$ [closed]

I have to draw a picture of $$\{ z\in\mathbb{ C } ; 0 < \arg[ (1-i)\overline z ] \le \frac \pi 4 \}$$ I totally don't get it and i don't even know how to start solving this.
1 vote
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### Geometric interpretation of this condition

In a Differential Equations context we have the following theorem: $\textbf{Theorem:}$ Let $D\subseteq\mathbb{R}^n$ be some open set and $f:D\to\mathbb{R}^n$ a $\mathscr{C}^1$ vector field. Then, for ...
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### Interpretation Reflection principle

The reflection principle says that for the Markov process $(B_t,\mathcal{F}_t,P_x)$ associated with Brownian Motion it is satisfied that $P_0(\text{max}_{s\leq t} B_s \geq a) =2P_0(B_t\geq a)$ ...
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### Corollary of Projection onto a closed convex set and geometric interpretation

I need help with geometric interpretation of this theorem and with the corollary of the theorem: Theorem: projection onto a closed convex set Let $K \subset H$ be a nonempty closet convex set. ...
1 vote
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### simplex $B^{-1} \cdot A_j$ tableau interpretation

In an iteration of the simplex tableau implementation, what is the interpretation of the columns $B^{-1} \cdot A_j$ underneath each variable $x_j$?
I'm trying to write a formula that represents the intersections points for $n$ circumferences. All of these circumferences intersect them to each other. Is there a good representation to explicit this ...
### Proof and Geometric intuition of $u \leq 2\ln(1+u)$ for $u \in [0,1]$.
How can I prove the inequality $$u \leq 2\ln(1+u)$$ for $u \in [0,1]$. What is the geometric intuition behind this inequality?