so L(x)= aL(X1) + bL(X2) + cL(X3) + dL(X4) + eL(X5) + fL(X6)
but the first 3 terms will always be zero...if that's true I just tried to multiply with a Y matrix posted below and did not get the zero diagonal matrix.
Y=
\begin{pmatrix} 2 & -1 & 0 \\ -1 & 1 & 5 \\ 0 & 5 & 3\end{pmatrix}...
L multiplies with a matrix (X) and get a matrix (Y) which has diagonal elements zero.
L*X=Y
so L(X4)*X4 = X4 so I had to compute a matrix L(X4) which multiplies with X4 matrix so the result becomes same matrix X4.
Guess this is not the way to go then...
Question: I know the 6 basis set so x in the equation is given. But I am not sure how get L for the basis set since "Y" is not given. I only found LX1 using the Y matrix but that is not a arbitrary matrix.
L = X Y-1
The basis matrix is:
B=
\begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1...
Homework Statement Let L(x) a linear operator defined by setting the diagonal elements of x to zero. What will be the representation of this operator to the following basis set? x E X. X denote the set of all real symmetric 3x3 matrices. Homework Equations
L*y=x
L=x*inv(y)...
How can I represent L(x) to the 6 symmetric basis set? I am to use the trivial basis set {1} for the range-space (R,R) to solve the problem.
The symmetric matrix is:
\begin
{pmatrix} a & e & d \\ e & b & f \\d & f & c \end{pmatrix}
Based o...
There is none since elements a23 & a32 is not related to any values of a,b,c,d,e & f. So, following is not the basis matrix:
\begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1\end{pmatrix}
The following set of basis are:
\begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0...