Introduction to Linear Algebra 笔记

 

CH4

The row space is perpendicular to the nullspace.(Ax=0)

When the original Ax=b has no solution, multiply by A^Tand solve A^TAx=A^Tb

When the original Ax=b has no solution, we can solve Rx=QTb, (A=QR；Q是正交矩阵，所以

 

Q^T=Q^-1)

triple product == determinant == volume

 

CH6

For each λsolve (A-λI)x=0 or Ax=λx to find an eigenvector x;

 

^{The procudct of the n eigencalues equals the determinant of A}

the sum of the n eigenvalues equals the sum of the n diagonal of A,(the sum along the main diagonal is called the trace of A):Σλ= trace = Σ_i=ja_ij