Adjoint of 3x3 Matrix

Compute adjoint of matrix

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Libraries:
Aerospace Blockset / Utilities / Math Operations

Description

The Adjoint of 3x3 Matrix block computes the adjoint matrix for the input matrix. For related equations, see Algorithms.

Ports

Input

Port_1 — Input matrix

3-by-3 matrix

Input matrix, specified as a 3-by-3 matrix, in initial acceleration units.

Data Types: double

Output

Port_1 — Output acceleration

3-by-3 matrix

Output acceleration, returned as a 3-by-3 matrix, in final acceleration units.

Data Types: double

Algorithms

The input matrix has the form of

$$A=\left[\begin{array}{ccc}{A}_{11}& A_{12}& A_{13}\\ A_{21}& A_{22}& A_{23}\\ A_{31}& A_{32}& A_{33}\end{array}\right]$$

The adjoint of the matrix has the form of

$$\begin{array}{l}adj(A)=\left(\begin{array}{ccc}+\left|\begin{array}{cc}{A}_{22}& A_{23}\\ A_{32}& A_{33}\end{array}\right|& -\left|\begin{array}{cc}{A}_{12}& A_{13}\\ A_{32}& A_{33}\end{array}\right|& +\left|\begin{array}{cc}{A}_{12}& A_{13}\\ A_{22}& A_{23}\end{array}\right|\\ -\left|\begin{array}{cc}{A}_{21}& A_{23}\\ A_{31}& A_{33}\end{array}\right|& +\left|\begin{array}{cc}{A}_{11}& A_{13}\\ A_{31}& A_{33}\end{array}\right|& -\left|\begin{array}{cc}{A}_{11}& A_{13}\\ A_{21}& A_{23}\end{array}\right|\\ +\left|\begin{array}{cc}{A}_{21}& A_{22}\\ A_{31}& A_{32}\end{array}\right|& -\left|\begin{array}{cc}{A}_{11}& A_{12}\\ A_{31}& A_{32}\end{array}\right|& +\left|\begin{array}{cc}{A}_{11}& A_{12}\\ A_{21}& A_{22}\end{array}\right|\end{array}\right)\\ \end{array}$$

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a