在线性代数中，相似矩阵是指存在相似关系的矩阵。相似关系是两个矩阵之间的一种等价关系。两个n×n矩阵A与B为相似矩阵当且仅当存在一个n×n的可逆矩阵P，使得：

P被称为矩阵A与B之间的相似变换矩阵。

相似矩阵保留了矩阵的许多性质，因此许多对矩阵性质的研究可以通过研究更简单的相似矩阵而得到解决。

判断两个矩阵是否相似的辅助方法：

1.判断特征值是否相等； 2.判断行列式是否相等； 3.判断迹是否相等； 4.判断秩是否相等； 以上条件可以作为判断矩阵是否相似的必要条件，而非充分条件。

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 operator under two different bases, with P being the change of basis matrix.

A transformation is called a similarity transformation or conjugation of the matrix A. In the general linear group, similarity is therefore the same as conjugacy, and similar matrices are also called conjugate; however in a given subgroup H of the general linear group, the notion of conjugacy may be more restrictive than similarity, since it requires that P be chosen to lie in H.