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The matrix basics can be found on the linear algebra page.

Prolog

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Factorization of a Matrix A in Triangular Matrices A=LU

U is a upper triangular matrix and L is a lower triangular matrix:

Elimination Matrix

With the elemintion matrix E21 it is possible to bring a 2×2 matrix A into the upper triangular form U.

Example

A=(E21)-1U = LU

(E21)-1 is the lower triangular matrix L.

Nilpotent Matrices

Matrix A is called nilpotent of grade n when An=0.

Example 3x3 Matrices

Example 4x4 Matrices

Schloss Waldeck
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The next page is about rotation matrices.

29.Mai 2021 Version 1.0
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