Conversion base vector
matrix-based (column) vector consisting of Jennifer
multiplied her eyes vector coordinate our eyes get vector coordinates
which seems to be a mouthful to achieve the reverse process because the matrix is from my grid to Jennifer network grid
but the language is again transformed into Jennifer's language to describe our description.
But from another angle to think about to suddenly realize
this process can be seen as our misunderstanding of Jennifer vector, that we have the same coordinate system
coordinates vector transform vector is she really want to express
Most will leave its original vector space spanned in a transformation, however, some special vector to stay in their sheets into a space meant for his role matrix just stretch or compress it. 
Then this vector is called a feature vector, which is stretched characteristic matrix corresponding to
the nature satisfy Av = λv, becomes the identity transformation (A-λI) v = 0 . We should find a vector v, such a new matrix having a nonzero solution.
Review: Since iff transform matrix represents the spatial dimension when compressed to a lower, only the presence of a nonzero vector, such that the product matrix and its zero vector. Space compression corresponding to the determinant of the matrix is zero
so det (A-λI) = 0 , which means, our goal is to find a λ such that the determinant is zero, then find the eigenvectors v. V A found in the corresponding transformation remain in its original sheets into a linear space, and stretched to its corresponding scalar value λ value.
Next is characteristic about the content group
if the basis vectors are eigenvectors happens, the eyes of Jennifer basis vectors as columns of the matrix.
For the interpretation of the diagonal matrix may be: all the basis vectors are eigenvectors, diagonal elements are the eigenvalues they belong. But this matrix, after all, is a special case.
But if n is a matrix of order n linearly independent eigenvectors (i.e., you can select a set of eigenvectors sake sufficient space)
then you can transform coordinate system, that the feature vector is a vector group (here, the effect of base change method)
remove you want to use as a new coordinate vector group (herein refers to two feature vectors), and then speak coordinates as a column matrix, the column is based transform matrix. In the write-yl right transformation matrix, the inverse write-yl left transformation matrix, the original transformation when you sandwiched between two matrices, the matrix obtained is representative of the same transformation, but vectors constructed from the new group coordinate system the angle of view.
This done using the sense that a feature vector
of the new matrix must be diagonal, and the diagonal elements of the corresponding eigenvalues.
This is because it is located basis vectors of the coordinate system only in a scaling transformation:
it is a set of basis vectors (also a feature vector) of a collection of features is referred to as the base.
Application: To calculate a matrix of non-specific power 100, wherein the base can first transform, the computing power 100 that coordinates and then converted to a standard coordinate system
(i.e. diagonalization)
but not all matrix They are similar diagonalization.
End Sahua
