dimensions jacobian matrix?
361724
The Jacobian matrix will have dimensions depending on what you have constructed the Jacobian for.  You'll need to supply a bit more information.
199628
Assuming, of course, that each of the vectors has 3 entries...\n\nDo you know how to put a matrix formed from those four vectors in row-echelon form?\n\nI'm trying to decide the best way to teach this to you, which is why I need to know if you know how to get the matrices in REF, but the final "Answer" is to see if three of those vectors are linearly independent. If three of them are linearly independent, then they must span R^3.\n\nFor your second question, no. Remember that a singular matrix is a square matrix that is not invertible. Therefore, a singular matrix will not have a pivot in every column, which means that the columns are linearly dependent, which means that the rank is less than the dimension. Any square matrix with a column that is all 0's will will be singular.
921006
Area = πab where a and b are the semi-major and semi-minor axis length
440750
Density Matrix.\n\ndiagonal part + nondiagonal part or\nstate probabilities + transition probabilities.
823237
There is several way to solve the problem, but I think it is easies, to find the parametric representation, and then use, that the scalar-product of the orientations-vectors is zero, if the line are perpendicular, and the orientations-vectors is linear depended if parallel.\n\nL1:  y = -½x-3 => (x,y)= (1,-½)*t+(0,-3)\n4x-2y+5 = 0 <=> y=2x+5/2=>\nL2: (x,y) = (1,2)*t + (0+5/2)\n\nbecause (1,-½)*(1,2)=1-1=0 the lines are perpendicular
584514
Use 'Gaussian elimination' to obtain a basis for the span of matrix columns or rows.\n\nhttp://en.wikipedia.org/wiki/Gaussian_elimination
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.
848509
http://mathworld.wolfram.com/johnsonsoli...
73219
Anyone with matrix background
827987
No, it's an independant variable (in the sense that it's not a linear combination of other variables such as length, mass, or charge) and, since it's linearly independant, it can be used as a dimension (or one of the spanning vectors) in a vector space.\n\n\nDoug
700308
Seems more like a vector analysis question to me.
1069671
yep...scalars multiply vectors component by component just like you have shown.  you can also show it by plotting out the original vectors, scaling them appropriately, adding them, and finding the resukltant components.
683859
hi, \n\ni don't know what it has to do with finite element analysis, but the rotation matrix form depends on whether you are working in 2 or 3 (or more) dimensions, and about what axis you are rotating.\n\nthere are examples of a 2-d rotation matrix and all 3 3-d rotation matrices on this page:\n\nhttp://mathworld.wolfram.com/RotationMatrix.html\n\nbasically, the way they work is you take a vector in cartesian coordinates, and operate on it with (in other words, multiply by) this matrix.  the vector that comes out has been rotated by whatever angle you put in.\n\ncheers !
827717
I presume that's a pair of 2x2 matrices?  The answer is B.  I hate just giving the answer, but I don't see any reasonable way to discuss matrix multiplication in this format.  Please be sure you understand WHY it's B before you turn it in.
529872
Easy H*D*W    H=Height D=Depth W=Width *= times\n\nUse the units cubed, if it is meters use m^3 as the unit of measurement
414419
http://www.math.niu.edu/~beachy/aaol/frames_index.html
851884
They are unitary vectors in that their magnitude = 1 so that i dot j = i dot k =j dot k =1 . one being unity.\n\nThey do not have _units_ like displacement, velocity, magnetic field strength associated with them as they are designed to provide a general standardised framework for vector analysis where the vector quantities manipulated may be any sort of physical vector property.