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Jun
12
comment Multiply the number $(1001)_{2}$ by 3 digit number
I have no idea what $F0$ actually is, in your problem description it doesn't occur. BTW, I now don't have the time to continue until in about 12 hours.
Jun
12
comment Multiply the number $(1001)_{2}$ by 3 digit number
OK, so it seems to just be a specific implementation of an adder. If so, and if I understand your circuit correctly, then no. As far as I can see, you add $9$ to your number, multiply by $2$, and add $F0$ (whatever that is). But neither $9a=2(a+9)$, nor $9a=2(a+9)+1$ for all $a\in\{0,…,7\}$.
Jun
12
comment Multiply the number $(1001)_{2}$ by 3 digit number
I admit that I don't know what a ripple carry adder is.
Jun
12
comment Multiply the number $(1001)_{2}$ by 3 digit number
If the goal is to make a circuit that multiplies a three-digit binary number with $9=1001_2$, instead of multiplying it with arbitrary 4-digit numbers, the minimal circuit doesn't even need gates.
Jun
12
answered Class of all finite sets
Jun
11
answered Probability of $x<y^2$ where $x$ and $y$ are uniformly distributed.
Jun
11
comment Probability of $x<y^2$ where $x$ and $y$ are uniformly distributed.
For $L=4$ this gives $160/3$, which is massively larger than $1$. Whatever you calculated, it's not a probability. I guess you should divide by $4L^2$. Also, your first integral result should have $2L^2$ instead of $2L$.
Jun
11
revised One-to-one and onto functions
added 1085 characters in body
Jun
11
comment One-to-one and onto functions
This looks like a homework question. If so, please add the homework tag.
Jun
11
answered One-to-one and onto functions
Jun
11
comment Given this transformation matrix, how do I decompose it into translation, rotation and scale matrices?
The upper left element of $S$ should be $-2\sqrt{2}$, not $-2/\sqrt{2}$.
Jun
10
comment Is there NO solution to this linear system of 3 equations, $3$ unknowns?
A simpler example would be $x+z=2$, $x=1$; there it's very obvious that it has a solution.
Jun
10
comment Is there NO solution to this linear system of 3 equations, $3$ unknowns?
The equation $0z=0$ has certainly solutions, despite containing, quite literally, an equation of the form $0z=\text{some number}$.
Jun
10
comment the product of a matrix and a permutation matrix
Well, think about it this way: How many vectors do you need to describe a matrix of rank $k$? (to make it more concrete, say you want to write it as $v_1v_1^T + \ldots + v_mv_m^T$; what is the minimum $m$ you need?) And now consider in the light of this what it means to lower the rank. Can you imagine to do that without throwing away information?
Jun
10
comment The definition of addition on the tensor product of Hilbert spaces
The fact that you cannot write a sum of tensor products as a single tensor product is at the heart of the whole field of quantum information. So a lot of people would be out of work if that were possible. :-)
Jun
10
comment the product of a matrix and a permutation matrix
Well, a very special matrix to alter the rank of $M$ is the matrix with only zero entries. Also, think about diagonal matrices with only ones and zeros on the diagonal. What do those do to $M$? More generally: What would you have to do to reduce the number of linearly independent vectors in $M$? And how might this be related to the eigenvalues of the matrix you multiply with $M$?
Jun
10
revised the product of a matrix and a permutation matrix
Improved formatting
Jun
10
answered the product of a matrix and a permutation matrix
Jun
9
comment Question about inner product
@AndrewSalmon: OK, done.
Jun
9
answered Question about inner product