Universal Identities I
... complicated identities, such as in linear algebra, where the polynomial identity viewpoint is really useful thanks to the following theorem involving complex numbers. Notice the (non-algebraic) topological hypothesis which occurs. Theorem 2.6. Let f (X1 , . . . , Xn ) and g(X1 , . . . , Xn ) be in C ...
... complicated identities, such as in linear algebra, where the polynomial identity viewpoint is really useful thanks to the following theorem involving complex numbers. Notice the (non-algebraic) topological hypothesis which occurs. Theorem 2.6. Let f (X1 , . . . , Xn ) and g(X1 , . . . , Xn ) be in C ...
Chapter 2 Systems of Linear Equations and Matrices
... your RREF matrix has 0’s on one side and a non-zero number on the other, you can straightaway say there is no solution. Now we can do some examples where the coefficient matrix is not square. When the matrix of coefficents is square we have the same number of variables as equations. When the number ...
... your RREF matrix has 0’s on one side and a non-zero number on the other, you can straightaway say there is no solution. Now we can do some examples where the coefficient matrix is not square. When the matrix of coefficents is square we have the same number of variables as equations. When the number ...
