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2024年4月16日发(作者：onclick事件是干什么的)

矩阵的合同变换的定义与性质

英文回答：

Definition of Congruence Transformation:

A congruence transformation, also known as a congruence

or similarity transformation, is a type of transformation

that preserves the shape and size of a matrix. In other

words, it is a transformation that does not change the

angles or lengths of the vectors in the matrix.

Properties of Congruence Transformations:

1. Preservation of Shape: A congruence transformation

preserves the shape of the matrix. This means that the

transformed matrix has the same number of rows and columns

as the original matrix.

For example, let's consider a 2x2 matrix:

Original matrix: A = [1 2]

[3 4]

If we apply a congruence transformation to this matrix

by multiplying it by a 2x2 matrix B, the resulting matrix C

will also have 2 rows and 2 columns:

Transformed matrix: C = B A = [a b]

[c d]

2. Preservation of Size: A congruence transformation

also preserves the size of the matrix. This means that the

transformed matrix has the same determinant as the original

matrix.

For example, let's consider the same 2x2 matrix A as

before. If we apply a congruence transformation to this

matrix, the determinant of the transformed matrix C will be

the same as the determinant of the original matrix A:


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