How to find eigenvector for a matrix?
113822
A 100 by 100 matrix has 100 eigenvectors. I would use some software to do this. This is too hard to do by hand. Buy the student version of MATLAB for example. You might be able to find some free software on the internet as well.
350722
The steps I followed were:  pick a vector in that subspace of R3, then find another vector perpendicular to that one that's still in R3.  These two should form a basis.  So, I picked (a,0,-a)to start from.  A vector perpendicular to that one that's still in the subspace is (a,2a,a).  \n\nA more general way to  find a basis (not necessarily normal) would be to pick a vector in that subspace, and then pick another one.  If the only solution of the equation A(vector 1)+B(vector 2)=0 is A=B=0, the two vectors are linearly independent, and form a basis for the subspace.
554827
Well, I suppose you want a program that computes the trace of a matrix. The trace is simply the sum of the elements in the diagonol in a matrix. I won't show it to you with OOP since there's no reason to.\n\nint trace(int matrix[][],int numrows,int numcols) {\n\nint tracetotal = 0;\n\nif (numcols != numrows) {\nstd::cout<<"Error: Can't compute trace. Not square matrix.&#92;n";\nexit(1);\n}\n\nfor (int i = 0; i < numrows; i++) {\ntracetotal+=matrix[i][i];\n}\n\nreturn tracetotal;\n}
61844
When we ask for an inverse matrix, we want a new matrix that, when multiplied by the given matrix, will give the identity matrix.  To find this matrix, we can proceed as follows:\nWrite down your matrix and write the identity matrix to the right of it.\n|4  -1|   |1   0|\n|3   5|   |0   1|\nNow the objective is to perform operations on the rows of the matrix to get it to look like the identity matrix, while doing the same operations on the nearby identity matrix.  Like so:\nMultiply the top row by 5.\n|20  -5|   |5   0|\n|3    5|   |0   1|\nNow add the rows together and put them on the top row.\n|23  0|   |5   1|\n|3   5|   |0   1|\nNow divide the top row by 23.\n|1   0|   |5/23  1/23|\n|3   5|   |0        1|\nNext, multiply the top row by -3 and add it to the bottom row (combining steps)\n|1   0|   |5/23     1/23|\n|0   5|   |-15/23  20/23|\nFinally, divide the bottom row by 5\n|1   0|   |5/23   1/23|\n|0   1|   |-3/23  4/23|\nLet's test our result.  Multiply the given matrix by our supposed inverse matrix.\n|4   -1|   |5/23   1/23|\n|3    5| x |-3/23  4/23|\nRemember to use matrix multiplication:\n|20/23+3/23   -4/23+4/23|\n|15/23-15/23  3/23+20/23|\nWhich is equal to\n|1   0|\n|0   1|\nThe identity matrix. So your inverse matrix is:\n|5/23   1/23|\n|-3/23  4/23|\nYou're welcome.
964615
Please type smith's algorithm for polynomial matrices at yahoo search you get links hope fully one of them should provide you with a solution.
37157
A covariance matrix is a useful tool in statistics. \n\nA matrix is an array of numbers, in the form of a rectangle, with several rows and several columns. A covariance matrix is a special kind of matrix that is used to find connections between variables. \n\nFor example, if you have N random variables, and you want to know how they are related to each other, then you can compute a covariance matrix. The covariance matrix for N random variables has N rows and N columns, that is, it is an N x N matrix. Note that the covariance matrix is a square matrix (it has the same number of rows and columns; in this case, N).\n \n\nThe diagonal elements of the covariance matrix give the variance of each of the random variables in turn; that is, they describe how much each of these random variables varies. \n\nThe off-diagonal elements describe how the random variable Xj corresponding to the jth row and the random variable Xk corresponding to the kth column behave. For example, if changes in Xj do not have any effect on Xk, then the covariance matrix value at row j and column k, C(j,k) will be zero: C(j,k)=0. If when Xj increases, Xk increases, then C(j,k)>0. If increasing Xj causes Xk to decrease, then C(j,k)<0.\n\nOf course, the details about how to compute the covariance matrix C(j,k) are slightly more complicated than this, but this gives you a sort of idea about what the covariance matrix means.
846282
here's an example\n\nwe want to reduce a matrix to u/t form\n\n1  10  -3       r1\n1  10   2       r2\n1  4     2       r3\n\n1  10  -3\n0  0     5      \n0  -6    5      \nr2-r1 \nr3-r1\n\n1  10  -3\n0  -6   5\n0   0   5      \n interchange rows 2 and 3\n\nupper triangular form\n\nthis is known as gaussian elimination\nand is used in solving systems of equations\n\ngo to the site:\n\nhttp://mathworld.wolfram.com/GaussianElimination.html\n\nthis gives a good example\n\nyou can also get help with other matrix\noperations at this site,plus access to the\nintegrator as well\n\ni hope that this helps
1126894
This normally means that you are going to be using Gaussian (or Gauss-Jordan) reduction, where ther eare three "moves" that are allowed.\n\n1) You can switch any two rows in the matrix.\n2) You can multiply any row in the matrix by a non-zero scalar.\n3) You can add a multiple of one row to another.\n\nUsing these three "moves," the goal is to reduce the matrix into a usable form (the echelon form, for example).
707729
The maximum order of a eigen vector is equal to the dimention of the matrix.\n\ni.e for a square matrix of dimention nxn, the maximum order of eigen vector is n.\n\nFor example if there is a 3x3 matrix then the maximum order of its eigen vector is 3.
830322
I just noticed that two rows are the same, right?  This is big, but I'll have to study up what it means.  Intuitively, I think that it means that the matrix has a null space, and thus and eigenvalue of zero.  \n\nor is it a type?\n\n\nRead up on it:\n\nhttp://en.wikipedia.org/wiki/Jordan_normal_form
314857
you should try to learn reading any book about vector analysis.\nSomething about vectors:\nhttp://mathworld.wolfram.com/topics/VectorAlgebra.html
574351
First, find the matrix of coefficients and it's determinant...\n\n|1 -4|\n|4 -1|  D = 1*-1 - 4*-4 = 15\n\nThen the column of answers...\n\n|4|\n|1|\n\nSubstitute the column of answers in for the first column, and find the determinant...\n\n|4 -4|\n|1 -1|  Dx= 4*-1 - -4*1 = 0\n\nRepeat for 2nd column...\n\n|1 4|\n|4 1|  Dy= 1*1 - 4*4 = -15\n\nCramer's Rule states x = Dx/D and y = Dy/d\n\nSo... x = 0 / 15 = 0\nAnd.. y = -15/15 = -1\n\nAnd there ya go :)
551932
Assuming your matrix is of order nxn and you want submatrix of order mxm.\n\nThen there is (n-m+1)^2 submatrices.\n\nSo you can run this loop(Java code)\n\nfor(i=0;i==n-m;i++)\n{\nint k;\nfor(k=0;k==n-m;k++)\n{\nint p,q;\nfor(p=0;p<m;p++)\n{\nfor(q=0;q<m;q++)\n{\nprint("  ");\nprint(a[p][q]);\n}\nprintln();\n}\n}\n\n}\n\nTo print all the submatrices iterate over this procedure canging m from 1 to n.
802863
| A - I(lamda)| = 0 ==> eigenvalue ... \n\nlamda is an eigenvalue...\n\nsolve the matrix first
159293
Depends on what you are analyzing.  Matrix algebra is used extensively in communications and signal processing applications.  Not very much, though, in financial applications.
4598
Recall that the eigenvalues are the values of x such that det(xI-AB)=0.  Also det is a multiplicative function.  So eigenvalues are the values of x such that det(xA^(-1)-B)=0 (left multiply by A^(-1)).  But these are the same values of x such that det(xI-BA)=0 (right multiply by A.
268402
Consider the matrix of the real parts of a Hermitian matrix as A and the matrix of the imaginary parts as B. Use the definition of Hermitian.\nAnother hint: If a_ij = a+ib, what would a_ji have to be if the matrix A is Hermitian ? What is then true about the diagonal of a Hermitian matrix?