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Questions Asked

xEnOnn:
Group Title
How can I prove that it is true that \[det(AB)=det(A) \times det(B)\] where A and B are square matrices?
 updated 2 years ago
 7 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
When we say \[\frac{\mathrm{d} y}{\mathrm{d} x}\], it also be written as \[\Delta x\] or \[\Delta y\]?
 updated 2 years ago
 14 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
How do I expand this equation: \[(1+t+t^2)^5\]
I formed the equation into a binomial equation this way: \[(1+t+t^2)^5=\sum \binom{5}{r_1}\b…
 updated 2 years ago
 No Medals Yet
Mathematics

xEnOnn:
Group Title
From this: \[(1+t+t^2)^5=\sum \binom{5}{r_1}\binom{5r_1}{r_2}t^{r_2}t^{2r_1}\]
How do I carry on to find out the values of \[r_1\] and \[r…
 updated 2 years ago
 39 replies
 2 Medals
Mathematics

xEnOnn:
Group Title
How I show that the eigenvalues of matrix A times matrix B is and BA are equal? That's to show eigenvals(AB)=eigenvals(BA).
 updated 2 years ago
 4 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
Suppose I have this: \[A=P_{0}\Lambda P_{0}^{1}\]
And then there is a diagonal matrix D such that its determinant is always equals to 1:
\…
 updated 2 years ago
 No Medals Yet
Mathematics

xEnOnn:
Group Title
Given a quadratic equation say:
\[2x^{2}+8xy+7y^{2}>0\]
, how can I know that if the equation is true that it will always be more than zero…
 updated 2 years ago
 4 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
Suppose the eigenvalues of matrix A are p1 and p2 and the eigenvalues of matrix B are k1 and k2. When the two matrices are multiplied toget…
 updated 2 years ago
 No Medals Yet
Mathematics

xEnOnn:
Group Title
Can I say that all orthonormal matrices are symmetric?
 updated 2 years ago
 9 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
If a matrix has repeated eigenvalues of 0, can its eigenspace matrix still be independent? Although it is usually said that the eigenspace …
 updated 2 years ago
 No Medals Yet
Mathematics

xEnOnn:
Group Title
Is it possible for a symmetric matrix to have a negative eigenvalues? Or all symmetric matrices will ALWAYS have positive eigenvalues?
 updated 2 years ago
 5 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
It is said that if the matrix S is nonsingular and a matrix B is \[B=S\Lambda S^{1}\], then eigenvalues of matrix S and matrix B coincide…
 updated 2 years ago
 3 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
How can I show that the determinant of matrix A is the same as the determinant of the transpose of matrix A?
 updated 2 years ago
 4 replies
 3 Medals
Mathematics

xEnOnn:
Group Title
How can I prove that for all symmetric matrices, its inverse is also symmetric?
 updated 2 years ago
 36 replies
 4 Medals
Mathematics

xEnOnn:
Group Title
If all eigenvalues of a nxn matrix are positive, does it imply that the matrix is positive definite?
 updated 2 years ago
 22 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
If given that matrix A has the property \[A^{T}A$\] results in a matrix that is positive definite, what does this tell about the matrix A i…
 updated 2 years ago
 No Medals Yet
Mathematics

xEnOnn:
Group Title
If given that matrix A has the property
\[A^{T}A\]
results in a matrix that is positive definite, what does this tell about the matrix A it…
 updated 2 years ago
 No Medals Yet
Mathematics

xEnOnn:
Group Title
Let matrix B and A both be nxn symmetric matrices and C be any nxn nonsymmetric matrix then \[A=BCB^{T}\].
Then \[A^{T}=(BCB^{T})^{T}\]
\[…
 updated 2 years ago
 2 replies
 No Medals Yet
Mathematics

xEnOnn:
Group Title
If \[
A=\begin{bmatrix}
1 & 2 & 0\\ …
 updated 2 years ago
 18 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
To find the eigenvalues and eigenvectors, [\Ax=\lambda x\], must [\A\] always be an nonsingular matrix? Can matrix [\A\] be any rectangula…
 updated 2 years ago
 26 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
What does a dot vector operation tells about the 2 vectors? Say vector a dot vector b, if it doesn't give zero, what does the result of the…
 updated 3 years ago
 9 replies
 2 Medals
Mathematics

xEnOnn:
Group Title
Can I safely say that all n by n symmetrical matrices are invertible and therefore nonsingular?
 updated 3 years ago
 3 replies
 2 Medals
Mathematics

xEnOnn:
Group Title
If X and Y are both matrices, then how does \[(X+Y)^{T}\] evaluate? And if I further extend it to say \[(X+Y)^{T}(X+Y)\] then how would thi…
 updated 3 years ago
 3 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
The equation Ax=b is solvable exactly when b is a linear combination of the columns of A. So Ax=b is solvable exactly when b lies in the co…
 updated 3 years ago
 4 replies
 No Medals Yet
Mathematics

xEnOnn:
Group Title
What does it mean when it says b is a nontrivial linear combination of the columns of matrix A? What is trivial and nontrivial in this co…
 updated 3 years ago
 4 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
Can I safely say all diagonal matrices are invertible and hence nonsingular?
 updated 3 years ago
 4 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
How does the power of a matrix operate? If A is a matrix, [\A^{2}\] doesn't look like literally taking the powers of each entries in the ma…
 updated 3 years ago
 7 replies
 2 Medals
Mathematics

xEnOnn:
Group Title
Does the method LU Decomposition to solve for unknowns in a system of equation only work for \[Ax=b\] when there is only one solution \[x\]…
 updated 3 years ago
 2 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
It is said that all matrices of any rank=\[r\] can be created from a \[r\] number of rank 1 matrices. But I still don't understand how I ca…
 updated 3 years ago
 2 replies
 1 Medal
Mathematics

xEnOnn:
Group Title
If a matrix is not invertible, can I say the matrix has many solutions? Or is the matrix has many solutions as well as the possibility or n…
 updated 3 years ago
 13 replies
 2 Medals
Mathematics
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