ماتریسها و دترمینان
Matrices and Determinants
مباحث ماتریسها و دترمینانها.
جبر خطی کنکور ارشد علوم کامپیوتر
کارتها · 5
The bottom-right block H of M^(-1) satisfies det(M)det(H)=det(A), the diagonally opposite block.
Every square matrix satisfies its own characteristic polynomial; rearranging that polynomial expresses A^(-1) as a cheap polynomial in A — no cofactor matrix needed.
The determinant is linear in each row and alternating, so scaling a row scales it, swapping rows flips the sign, and any repeated row makes it zero — that is all you need to evaluate "transformed-matrix" determinant problems.
Factor out a common matrix power, then left- or right-multiply by its inverse to cancel it — only legal when that factor is invertible.
When an unknown matrix appears together with its transpose and trace, write it with literal entries, expand both sides entrywise, and turn the matrix identity into a small linear system.