1
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1answer
17 views

Cross-product is a left singular vector?

Assume A is a 3x2 matrix with rank(A)=2. u1 and u2 are already left singular vectors... How would I go about proving that the cross-product of the two is also a left singular vector? Hints would be ...
0
votes
2answers
42 views

About matrix $R$, what is this called: $R^TR$? What is it for?

I am doing singular value decomposition on a matrix $R$. The first step is to compute such a matrix $R^TR$. What is this matrix? A reference told me this is cross product of matrix R. I use a ...
1
vote
0answers
28 views

Matrix: Area of a Triangle, which point to choose for cross multiplication

When given 3 points(vertices), which one should you pick to do the your calculations with. E.g.: $P1=(1,-1,1) P2=(2,1,-1) P3=(1,-2,-1) $ I can pick P1 -> P2 and P1 -> P3. Then do my cross ...
3
votes
1answer
99 views

Show that $e^{\theta(s\times)} = I + \sin\theta(s\times) + (1 − \cos \theta)(s\times)^2$

$$e^{\theta(s\times)} = I + \sin\theta(s\times) + (1 − \cos \theta)(s\times)^2$$ I have to prove the above formula and am not sure where to start, may someone please help me! The full question is ...
2
votes
1answer
47 views

Unbiased estimate of cross-product for unbiased vector

Let $g$ be an unbiased estimate of a vector $G$. Can $g$ be used to find an unbiased estimate of the cross product $GG'$? I'm stuck because naively using $gg'$ is a biased estimator, with the ...
1
vote
1answer
89 views

Determining $u=v \times w$ using the cross product

Let $v = (3,0,0)$ and $w=(0,1,-1).$ Determine $u = v \times w$ using the geometric properties of the cross product rather than the formula. What are the possible angles $x$ between two unit vectors ...
2
votes
1answer
168 views

Multiplying vectors (answered own question)

I recently realised that asking a question and answering our own question is allowed here, so here is a question I've seen commonly on many sites: "How does one multiply two vectors?" This is very ...
4
votes
1answer
89 views

How to solve cross-products including matrices?

I'm a programmer and I'm doing a whitebalance-transformation in RGB colorspace. This should work with this transformation matrix that I've found in literature: $$ \begin{pmatrix} R \\ G \\ B ...
1
vote
1answer
42 views

Comparing a geometric definition of cross product to the “usual” one

Could you help me with my little problem? Given this definition of cross product: 1) $a \times b$ is perpendicular to $a$ and $b$, whenever $ a,b$ are linearly independent 2) basis $a, \ b, \ a ...
1
vote
1answer
256 views

Cross product and inverse of a matrix

I would like to show that $\left(\begin{array}{ccc} 1 & s & s^2 \\ 1 & t & t^2 \\ 1 & u & u^2 \end{array}\right)$ has an inverse provided $s$, $t$ and $u$ are distinct. I ...
5
votes
1answer
774 views

Cross product of vectors as a determinant: valid matrix operation?

"The definition of the cross product can also be represented by the determinant of a formal matrix." —Wikipedia This seems like a hack to me—something of much practical use but ...
2
votes
1answer
566 views

Orthogonal matrix over cross product

Is $Qa \wedge Qb = \pm Q(a \wedge b)$, where $a$ and $b$ are two unitary vectors in $E^3$ and $Q$ is an orthogonal matrix ??? Thanks