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- why geometric multiplicity is bounded by algebraic multiplicity?
The geometric multiplicity the be the dimension of the eigenspace associated with the eigenvalue $\lambda_i$ For example: $\begin{bmatrix}1 1\\0 1\end{bmatrix}$ has root $1$ with algebraic multiplicity $2$, but the geometric multiplicity $1$ My Question: Why is the geometric multiplicity always bounded by algebraic multiplicity? Thanks
- What does the dot product of two vectors represent?
It might help to think of multiplication of real numbers in a more geometric fashion $2$ times $3$ is the length of the interval you get starting with an interval of length $3$ and then stretching the line by a factor of $2$ For dot product, in addition to this stretching idea, you need another geometric idea, namely projection
- MLE of the Geometric Distribution - Mathematics Stack Exchange
Regrettably, there are two distributions that are called geometric [1], the classical one, taking values in $1,2,\ldots$ and the shifted variant that takes values in $0,1,2,\ldots$
- Sum of a power series $n x^n$ - Mathematics Stack Exchange
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- Geometric Algebra and the Gradient of a Vector
In geometric algebra we have the derivative by a vector of a vector field $$\nabla V=\nabla \cdot V+\nabla \wedge V$$ While in tensor analysis we have $$\nabla V=\frac{1}{n}I(n)\nabla \cdot V +\nabla \wedge V+\sigma (V)$$ where I(n) is the n-dimensional identity matrix and $\sigma (V)$ is the symmetric traceless part of the matrix associated
- expectation - Proof for Mean of Geometric Distribution - Mathematics . . .
3 Complete the summation (geometric series) 4 Complete the differentiation 5 Get your answer Questions: Is there anything wrong in arriving at the formula the way I have done Isn't it better to use the arithco-geometric formula then go through all that calculus just to convert an arithco-geometric series into a geometric one
- geometric series - Finding $S_n$ in terms of n for the sequence (6 + 66 . . .
Prove: in geometric sequence ($0\ <\ r\ <\ 1$) the ratio between a term and the sum of all following terms doesn't depend on the location of that term 2 Geometrical series extra term confusion
- Geometric interpretation and computation of the Normal bundle
Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
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