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consider a matrix A
obtain a transformation which will diagonalize the matrix.Whatare the coordinates of an arbitrary vector
a=traspos(x,y,z)
with respect to the basis set which diagonalizes A?
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4. Derive the matrix for inverse transformation.?
I could do that if you gave me the original matrix.
What does rotation mean in termsof inverse of orthogonal matrix?
The inverse of a rotation matrix represents a rotation in the opposite direction, by the same angle, about the same axis. Since M-1M = I, M-1(Mv) = v. Thus, any matrix inverse will "undo" the transformation of the original matrix.
Write the transformation matrix for 2D rotation?
For counterclockwise rotation, the matrix has the following elements. I will write (11) for the first row, first column etc. since there is no way to easily repesent a matrix here. We rotate by an angle theta. (11) is cos theta (12) negative sin theta (21) is sin theta and (22) is cos theta
What is an eigenvalue?
If a linear transformation acts on a vector and the result is only a change in the vector's magnitude, not direction, that vector is called an eigenvector of that particular linear transformation, and the magnitude that the vector is changed by is called an eigenvalue of that eigenvector.Formulaically, this statement is expressed as Av=kv, where A is the linear transformation, vis the eigenvector, and k is the eigenvalue. Keep in mind that A is usually a matrix and k is a scalar multiple that must exist in the field of which is over the vector space in question.
Is there any matrix called as zero matrix?
ya yes its there a matrix called zero matrix
the matrix sum below?
transformation
Difference between 3D transformation and 2D transformation?
difference between 2d and 3d transformation matrix
4. Derive the matrix for inverse transformation.?
I could do that if you gave me the original matrix.
When you multiply by a transformation it is multiplied on the left of the matrix?
somebody answer
Derive the matrix for inverse transformation in graphics?
reconvene
When you multiply by a transformation it is multiplied on the left of the vertex matrix?
not all the time
What does rotation mean in termsof inverse of orthogonal matrix?
The inverse of a rotation matrix represents a rotation in the opposite direction, by the same angle, about the same axis. Since M-1M = I, M-1(Mv) = v. Thus, any matrix inverse will "undo" the transformation of the original matrix.
Which specific linear algebraic and related mathematical techniques are employed in geometric transformation?
Matrix multiplication is the most likely technique.
How do you determine the invariant point in a transformation of a relation?
the invarient point is the points of the graph that is unaltered by the transformation. If point (5,0) stays as (5,0) after a transformation than it is a invariant point The above just defines an invariant point... Here's a method for finding them: If the transformation M is represented by a square matrix with n rows and n columns, write the equation; Mx=x Where M is your transformation, and x is a matrix of order nx1 (n rows, 1 column) that consists of unknowns (could be a, b, c, d,.. ). Then just multiply out and you'll get n simultaneous equations, whichever values of a, b, c, d,... satisfy these are the invariant points of the transformation
Explain Shearing and reflection as a technique of 2d transformation?
ShearingFor shear mapping (visually similar to slanting), there are two possibilities. For a shear parallel to the x axis has x' = x + ky and y' = y; the shear matrix, applied to column vectors, is: A shear parallel to the y axis has x' = xand y' = y + kx, which has matrix form:ReflectionTo reflect a vector about a line that goes through the origin, let be a vector in the direction of the line: To reflect a point through a plane ax + by + cz = 0 (which goes through the origin), one can use , where is the 3x3 identity matrix and is the three-dimensional unit vector for the surface normal of the plane. If the L2 norm of a,b, and c is unity, the transformation matrix can be expressed as:Note that these are particular cases of a Householder reflection in two and three dimensions. A reflection about a line or plane that does not go through the origin is not a linear transformation; it is an affine transformation.
Write the transformation matrix for 2D rotation?
For counterclockwise rotation, the matrix has the following elements. I will write (11) for the first row, first column etc. since there is no way to easily repesent a matrix here. We rotate by an angle theta. (11) is cos theta (12) negative sin theta (21) is sin theta and (22) is cos theta
Find a transformation matrix which aligns a given vector Vabc with the vector K along the positive z axis?
[abc][k] [10] [a,-b] [01] [-c,k]
