求解一个矩阵方程，即一个由 16 个方程组成的系统，其中 16 个未知：调用求解函数时出错

如何解决求解一个矩阵方程，即一个由 16 个方程组成的系统，其中 16 个未知：调用求解函数时出错

我想知道在什么条件下两个 4x4 矩阵之间可以相等。

我构建了 2 个矩阵，我想从中获得相等性。

但是为了得到这个等式，我必须解决一个未知矩阵 4x4，它的项出现在 2 个矩阵 4x4 中。

为了给你展示一个实际的例子，我在下面放了一个小的 Matlab 脚本，它试图遵循上面解释的所有推理：

clear;
clc;

% Big_1 Fisher : 
FISH_Big_1_SYM = sym('sp_',[5,5],'real');
% Force symmetry for Big_1
FISH_Big_1_SYM = tril(FISH_Big_1_SYM.') + triu(FISH_Big_1_SYM,1);

% Big_2 Fisher : 
FISH_Big_2_SYM = sym('sp_','real');
% Force symmetry for Big_2
FISH_Big_2_SYM = tril(FISH_Big_2_SYM.') + triu(FISH_Big_2_SYM,1);

% Jacobian 1 
J_1_SYM = sym('j_','real');
% Jacobian 2 
J_2_SYM = sym('j_','real');

% Remove 4th row/column
J_2_SYM(4,:) = [];
J_2_SYM(:,4) = [];

%%%%%%%% Method 1 : projection before marginalisation %%%%%%%%%

% Projection
FISH_proj_1 = J_1_SYM'*FISH_Big_1_SYM*J_1_SYM;
% Check size : 5x5
size(FISH_proj_1)
% Invert Fisher_2
COV_Big_1_SYM = inv(FISH_Big_1_SYM);
% Marginalisation
COV_Big_1_SYM(4,:) = [];
COV_Big_1_SYM(:,4) = [];
FISH_Big_1_SYM = inv(COV_Big_1_SYM);


%%%%%%%% Method 2 : projection after marginalisation %%%%%%%%%
% Invert Fisher_2
COV_Big_2_SYM = inv(FISH_Big_2_SYM);
% Remove 4th row/column
COV_Big_2_SYM(4,:) = [];
COV_Big_2_SYM(:,4) = [];
% Re-inverse
FISH_Big_2_SYM_new = inv(COV_Big_2_SYM);
% Projection 2x2
FISH_proj_2 = J_2_SYM'*FISH_Big_2_SYM_new*J_2_SYM;
% Check size : 4x4
size(FISH_proj_2)


% Remove 4th row/column of Fisher matrix method 1
FISH_proj_1(4,:) = [];
FISH_proj_1(:,4) = [];

% Test equality between 2 matrices
isequal(FISH_proj_1,FISH_proj_2);

% Matricial equation to solve
eqn = FISH_proj_1 == FISH_proj_2;

% Solving : Jacobian 4x4 unknown
[solx,parameters,conditions] = solve(eqn,J_2_SYM,'ReturnConditions',true);
solx

完成构建我的 2 个矩阵 FISH_proj_1 和 FISH_proj_2 后，我在“解决”函数中收到错误：

Error using sym/solve (line 279)
Inconsistent output with 1 variables for input argument with 16 variables.

Error in demo_projection_dev (line 62)
[solx,true);

未知数是一个名为 J_2_SYM 的矩阵 4x4。

如何使用解决功能调试此错误？如果我将 J_2_SYM unknown 直接放在 solve 函数调用中，语法是否正确？