2x2 matrix calculation

Dear all,

I want to solve the 2x2 matrix problem.

There are three 2x2 matrix (Ta, Tb, Tc). Two matrix are known and one matrix is unknown value.

For example Ta = [3 4 ; 4 3], Tb=[1 2 ; 2 1], Tc=[x y ; y x].

Can I solve the Tc, when I have equation with Ta=Tc * Tb * Tc.

Thank you~!

Answer 1

[Sam Chak]

Hi @dhlee

Maybe you can solve the problem like this?

syms x y

Ta = sym('Ta', [2 2]);
Tb = sym('Tb', [2 2]);
Tc = sym('Tc', [2 2]);

Ta = [sym('3') sym('4'); sym('4') sym('3')]

Ta = 

Tb = [sym('1') sym('2'); sym('2') sym('1')]

Tb = 

Tc = [x y; y x]

Tc = 

Meqn = Ta - Tc*Tb*Tc

Meqn = 

eqns = [Meqn(1, 1) == 0, Meqn(1, 2) == 0];
[xsol, ysol] = solve(eqns)

xsol = 

ysol = 

x = double(xsol)

x = 4×1

-0.2638 -1.2638 1.2638 0.2638

y = double(ysol)

y = 4×1

-1.2638 -0.2638 0.2638 1.2638

% Check if correct
TB = [1 2; 2 1];
TC = [x(3) y(3); y(3) x(3)];
TA = TC*TB*TC

TA = 2×2

3 4 4 3

[dhlee]

Thank you for your quick solution~! ^^

I installed symbolic math toolbox for using the syms.