9. We saw how JNF generalizes the notion of diagonalization, and we will now look at...
9. We saw how JNF generalizes the notion of diagonalization, and we will now look at a similar concept which generalizes the notion of an inverse. The matrix pseudo-inverse of A E Mmxm(R) is the matrix At E Mmxm(R) which satisfies the following four properties (a) AA+A= A (b) A+AA+ = A+ (c) (AA+)T = AA+ (d) (A+A)T = A+A Quickly convince yourself that this is indeed a generalization of the notion of A-1. The following is true: Any matrix...
s={(8.60) :) :) is a basis of M3x2(R)? (d) (1 point) The set = {(1 9:(. :) : 6 1) (1 1) (1 :) :()} is linearly independent. (e) (1 point) For a linear transformation A:R" + Rd the dimension of the nullspace is larger than d. (f) (1 points) Let AC M4x4 be a diagonal matrix. A is similar to a matrix A which has eigenvalues 1,2,3 with algebraic multiplicities 1,2, 1 and geometric multiplicities 1,1, 1 respectively. 8....
Could someone pls explain question 9 (e)? 9. Consider the set of matrices F = a) Show that AB BA for all A, B E F b) Show that every A E F\ {0} is invertible and compute A-. c) Show that F is a field d) Show that F can be identified with C e) What form of matrix in F corresponds to the modđulus-argument form of a complex number Comment on the geometric significance. Solution a) Let A...
TSD.1 In this problem, we will see (in outline) how we can calculate the multiplicity of a monatomic ideal gas This derivation involves concepts presented in chapter 17 Note that the task is to count the number of microstates that are compatible with a given gas macrostate, which we describe by specifying the gas's total energy u (within a tiny range of width dlu), the gas's volume V and the num- ber of molecules N in the gas. We will...