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Mar
17
answered Finding a Closed Form of a Two Dimensional Recurrence
Mar
17
comment Finding a Closed Form of a Two Dimensional Recurrence
Is the intent for $a_{n,m}$ with $n \ge m$? Otherwise it seems $a_{2,1} = -1/2$? In other words, if you don't want to define it for $n > m$, the first initial condition only gives $a_{1,1}$, no?
Mar
17
reviewed Approve suggested edit on Multually exlcusive + indpedent random variable?
Mar
17
comment maximum value of the determinant
Interesting. They certainly should be linearly independent, otherwise the determinant is 0. I assume if you have orthogonal ones, it maximizes the determinant, but not sure why that happend geometrically. Can we related $det(A)$ to the angle between the columns, in the $2 \times 2$ or $3 \times 3$ case? The only thing is can think about is that determinant is the product of eigenvalues...
Mar
17
answered Poisson Distriburion
Mar
17
revised Poisson Distriburion
added 63 characters in body; edited tags
Mar
17
revised Calculate the length of the line which represents the function in a plot
added 324 characters in body
Mar
17
comment Calculate the length of the line which represents the function in a plot
@QuanticProgramming added a graph and some notes to make some intuition.
Mar
17
revised Calculate the length of the line which represents the function in a plot
added 324 characters in body
Mar
17
revised Proof that $f(x)=x^{1/n}$ is continuous.
added 207 characters in body; edited tags; edited title
Mar
17
comment Prove that — the range $R(T)$ of a bounded linear operator $T:X\to Y$ need not be closed in $Y$
Hi, welcome to Math.SE! Please add your thoughts on how to approach the problem and we will be glad to give some hints.
Mar
17
revised Prove that — the range $R(T)$ of a bounded linear operator $T:X\to Y$ need not be closed in $Y$
added 8 characters in body; edited tags; edited title
Mar
17
comment 2 out of 3 or 5 out of 8
@user3344591 exactly.
Mar
17
answered How to resolve this diferential equation $y^2 y^{\prime}=x^3$
Mar
17
comment Calculate the length of the line which represents the function in a plot
@QuanticProgramming Not sure if the one I typed in is so wild really. Under real values of $a$, you get real output. not sure why it is a problem?
Mar
17
answered Calculate the length of the line which represents the function in a plot
Mar
17
answered Is this $f(x)$ answer correct in regards to functions?
Mar
12
comment Integral of composition
Your $f(x)$ is not strictly increasing.
Mar
12
comment Meaning of a regular matrix
@Adam correct, $V$ is indeed the eigenvector matrix (in which you rescale every column to be of norm $1$). Multiplication by $V$ can be seen as changing from the space in which the coordinates are given by the standard basis to the space where the coordinates are given by the eigenvalues, which are also a basis.
Mar
12
comment Meaning of a regular matrix
@GerryMyerson You can interpret singular value decomposition in a similar vein, it is much more general. Even then it won't cover all cases, but it does take care of a very large subclass, and creates intuition to build on for the other ones.