Linear algebra

Linear algebra

1. Matrix

   • A rectangular array of numbers, arranged in rows and columns.
   • Eigenvalues
     • These are special values for the matrix.  How come? Here is a matrix multiplication: A(matrix) v(vector) b(scalar) Av=bv It can be possible to find scalar values like b that when multiplying a special vector v, it acts as if it were matrix A. This is what makes it special.
     • Jacobian method
   • Similarity transformation
     • A->XAX^-1
       • This new matrix has the same eigenvalues as A. It also has similar eigenvectors, determined by X ( u= Xv) so v = X^-1 u