Matrix Similarity

Matrix Similarity

In linear algebra, two n-by-n matrices A and B are called similar if

for some invertible n-by-n matrix P. Similar matrices represent the same linear transformation under two different bases, with P being the change of basis matrix.

The matrix P is sometimes called a similarity transformation. In the context of matrix groups, similarity is sometimes referred to as conjugacy, with similar matrices being conjugate.

Read more about Matrix Similarity:  Properties

Famous quotes containing the words matrix and/or similarity:

    As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.
    Margaret Atwood (b. 1939)

    Incompatibility. In matrimony a similarity of tastes, particularly the taste for domination.
    Ambrose Bierce (1842–1914)