This is a TRUE-FALSE Question with justification.
If Q is an orthogonal n×n matrix, then Row(Q)...
This is a TRUE-FALSE Question with justification.
If Q is an orthogonal n×n matrix, then Row(Q) =
Col(Q).
The Answer to this is TRUE. I want to know a solid
reasoning/explanation for it.
In one of the answers, it says that " Since Q is orthogonal,
QTQ = I, so Q is invertible, hence Row(Q) = Col(Q) =
Rn. But my question is: Why is it that for an invertible
matrix, Row(Q) = Col (Q) ?
Any other explanation that...
Find an orthogonal matrix P such that a change of variables, x =
Py, where x...
Find an orthogonal matrix P such that a change of variables, x =
Py, where x = [x1, x2] , y = [y1, y2] , transforms the quadratic
form 6x1^2+ 4x1x2 + 3x2^2 into one with no cross-product term.
Write down the new quadratic form.
1. Find the orthogonal projection of the matrix
[[3,2][4,5]] onto the space of diagonal 2x2 matrices...
1. Find the orthogonal projection of the matrix
[[3,2][4,5]] onto the space of diagonal 2x2 matrices of the form
lambda?I.
[[4.5,0][0,4.5]] [[5.5,0][0,5.5]] [[4,0][0,4]] [[3.5,0][0,3.5]] [[5,0][0,5]] [[1.5,0][0,1.5]]
2. Find the orthogonal projection of the matrix
[[2,1][2,6]] onto the space of symmetric 2x2 matrices of trace
0.
[[-1,3][3,1]] [[1.5,1][1,-1.5]] [[0,4][4,0]] [[3,3.5][3.5,-3]] [[0,1.5][1.5,0]] [[-2,1.5][1.5,2]] [[0.5,4.5][4.5,-0.5]] [[-1,6][6,1]] [[0,3.5][3.5,0]] [[-1.5,3.5][3.5,1.5]]
3. Find the orthogonal projection of the matrix
[[1,5][1,2]] onto the space of anti-symmetric 2x2
matrices.
[[0,-1] [1,0]] [[0,2] [-2,0]] [[0,-1.5]
[1.5,0]] [[0,2.5] [-2.5,0]] [[0,0]
[0,0]] [[0,-0.5] [0.5,0]] [[0,1] [-1,0]]
[[0,1.5] [-1.5,0]] [[0,-2.5]
[2.5,0]] [[0,0.5] [-0.5,0]]
4. Let p be the orthogonal projection of
u=[40,-9,91]T onto the...