0
votes
0answers
33 views

How can this equation be solved with respect to mu?

How can this equation be solved with respect to mu? I'm not even sure whether this equation can be solved or not. If it's not possible, could you explain why?
1
vote
1answer
39 views

What can I do to this expression to lose the summations?

I'm at the end of a past paper question and need to derive this answer: I am very close and have got to this by doing d/dx to the * equation: What can I do to get rid of these summation signs ...
1
vote
3answers
34 views

Using $S_n = \sum_{k=1}^{n}H_k$ where $H_k$ are the harmonic numbers, show $S_n = (n+1)H_n - n$ [duplicate]

The question: Using $S_n = \sum_{k=1}^{n}H_k$ where $H_k$ are the harmonic numbers, show $S_n = (n+1)H_n - n$. So far I have $S_n = \sum_{k=1}^{n} H_k = \sum_{k=1}^{n} ...
1
vote
4answers
84 views

Algebra-sum of entries in each column of a sqaure matrix = constant

This is a question from an algebra homework and I am just looking for some tips. The question is: We have: $M$: an $n\times n$ matrix with real entries $c$: a real constant the ...
0
votes
2answers
79 views

Raising $e$ to the power of a matrix

Does there exist a definition for matrix exponentiation? If we have, say, an integer, one can define $A^B$ as follows: $$\prod_{n = 1}^B A$$ We can define exponentials of fractions as a power of a ...
0
votes
2answers
74 views

Find the symmetric matrix that represents the quadratic form $Q(X)=trace(X^2)$, $X\in mat_n\mathbb (R)$

as the title says, find the symmetric matrix (or signature) of $Q(X)=trace(X^2)$ where $X$ is an $n$ by $n$ matrix with real entries. the diagonal of $X^2$ is $$\sum_{k=1}^n x_{ik}x_{ki}$$ So ...
3
votes
1answer
94 views

Signature of quadratic form $Q(p)=p(1)p(2)+p(3)p(4)$

I was asked to find the signature of the quadtratic form $Q(p)=p(1)p(2)+p(3)p(4)$ where $p$ is a polynomial in $\mathbb R_n[x]$ I tried doing it via finding the symmetric matrix that $Q$ corresponds ...
6
votes
2answers
130 views

What can be computed by axiomatic summation?

Here are three simple properties one might require of a summation method for divergent series: A stable summation scheme is one in which (assuming also each sums are defined iff the other is) ...
0
votes
3answers
100 views

Proof involving a summation

How would I go about proving that $\sum_{i<j} 1 $ = $ n\choose 2$ and $$ \sum_{i<j}(x_i +x_j) = (n-1)\sum x_i $$ I understand the intuition behind the statements. I'm just unsure of how to ...
0
votes
2answers
57 views

Is there any formula for summation?

$$0.01\sum_{x=1}^{30}(0.99)^{x-1} = 1-0.99^{30}$$ I wonder if there is a formula for summation and I want to know. Would anyone mind telling me? It would be better for me to solve problems, like the ...
2
votes
3answers
61 views

Why do I see i and k as the indices of summation?

I'm working on linear algebra and just wanted to clear up an uncertainty regarding whether there is a difference in the use of i and k as the dummy variables for the index of summation? ...
1
vote
2answers
48 views

Help with summation question?

I have a problem involving sums: I just have no idea how to solve this. I know how to solve sums but this does not make sense to me. I need the value of the 'a' but in the first one, 'a' must be ...
2
votes
1answer
35 views

Summing infinite numbers of matrices

Let $\mathbf{I}$ be a identity matrix, and $\mathbf{A}$ be a symmetric matrix in which every entry $a_{ij}$ follows $0 \le a_{ij} < 1$. I want to get $\mathbf{S} = \mathbf{I} + \mathbf{A} + ...
0
votes
3answers
177 views

Derivative of a summation in order to minimize

I am asked to minimize $\sum^n_{i=0}(x_i - C)^2$ with respect only to C so I know I have to take the derivative respect to C, set it equal to 0, and then solve. I have never done summation in my ...
2
votes
1answer
93 views

Finding the summation of the floor of the series.

Can someone help me the summation of the given series. $$\sum_{i=1}^n\left\lfloor\frac{n}i\right\rfloor$$ Negative of the above summation looks similar to the expansion of the $\log(1-x)$ without ...
1
vote
0answers
88 views

Compute $(-1)^n\sum_{k=1}^n (-1)^k\frac{(k+n-1)!}{(k-1)!(k-1)!(n-k)!}$

Compute $(-1)^n\sum_{k=1}^n (-1)^k\frac{(k+n-1)!}{(k-1)!(k-1)!(n-k)!}$ Define $a_{k,m}=\frac{(-1)^{k+m}(n+k-1)!(n+m-1)!}{(k+m-1)[(k-1)!(m-1)!]^2(n-m)!(n-k)!}$ Compute ...
1
vote
2answers
382 views

How to calculate weight of positive and negative values.

We have used formula formula to calculate weight as, $$ w_1 = \frac{s_1}{s_1 + s_2 + s_3};$$ $$ w_2 = \frac{s_2}{s_1 + s_2 + s_3};$$ $$ w_3 = \frac{s_3}{s_1 + s_2 + s_3};$$ However, their is ...
2
votes
1answer
45 views

(CHECK) Cardinality of Terms in the Expansion of a Product of Multinomials

QUESTION: How many terms are there in the expansion of $$(x+y)(a+b+c)(e+f+g)(h+i)$$ I'd like some help with this one, but I'd also like to discuss a method of generalization on the problem, ...
2
votes
1answer
78 views

Proof of correctness of Putzers algorithm

I have a question regarding the proof (seen below) of Putzers algorithm for matrix exponentiation. It's written by our danish lecturer at the university, so I translated the important parts into ...
1
vote
0answers
79 views

Simplifying expression

I am looking for a way to simplify this expression: $$ \sum_{i=0}^{n-k-1} \sum_{j=0}^{k-1} \left[ {n-k-1 \choose i} {k-1 \choose j} ((-1)^{k-1-j} - (-1)^{n-k-1-i}) \times {(n+0.5)! \over ...
0
votes
0answers
33 views

Finding solutions to the equation

I want to find possible solution satisfying both the equation: $\sum_{i=1}^{n} f_i^{2} = n$ $\sum_{i=1}^{n} f_i=0$ As the number of equations less than number of variables can we just comment on ...
5
votes
1answer
168 views

eigenvalues of the sum of a matrix with known eigenvalues and a diagonal matrix

Suppose $B = A+D$, where all the eigenvalues of $A$ are already known and $D$ is a diagonal matrix, how to compute the eigenvalues of B without diagonalizing $B$ directly?
-1
votes
3answers
22 views

Summation of non-null value [closed]

Sorry, am a bit rush of time, the main question in the picture.. How should I express the situation in the picture in a concise expression? Summation doesn't help as it does not skip the null value. ...
2
votes
3answers
719 views

What's the rule for solving nested sums?

I have the following nested double sum : $\sum_{t=1}^{T}\sum_{u=t}^{T} Z(u) \cdot (1+i)^{-u}$ with $0<i<1$ and $Z(u)$ being a non-specified function. By working with an example of $T=3$ I ...
1
vote
1answer
86 views

Simplify the expression

The below expression has three summations (sigmas) and $L$ is a real-matrix and symmetric, $X$ is a real matrix with $n$ rows and $X_{p\mathbb{.}},X_{q\mathbb{.}}$ denote the $p$ and $q$ rows of ...
0
votes
1answer
93 views

find the multiplicative factor for get a specific amount of sum on sin

i am not a math guru so please sorry if this is a silly question. i'm not sure on how to latexize this question so i've done a spreadsheets with openoffice (and i'm interest also in the best way to ...
4
votes
2answers
1k views

Smallest eigenvalues of Sum of Two Positive Matrices

Let $C = A + B$, where $A$, $B$, and $C$ are positive definite matrices. In addition, $C$ is fixed. Let $\lambda (A)$, $\lambda (B)$, and $\lambda (C)$ be smallest eigenvalues of $A$, $B$, and $C$, ...