Chapter 1

1.4: 1-8

• Due 9/27 - Problems 1,5 are to be carefully written up and separated from the rest of the HW.
  
  
• for 6, the line over γ means complex conjugate: If γ=a+bi, then conj(γ)=a-bi. The key properties of the conjugate that need verification are that
  conj(γ₁γ₂)=conj(γ₁)conj(γ₂) and conj(γ₁+γ₂)=conj(γ₁)+conj(γ₂). Also if γ is real, note that conj(γ) = γ since the imaginary part of γ is 0.
• Solutions

1.5: 1-3,5-7,9-11

• Due 10/4
• for 2, p₀≠ 0.
• for 8, identify x_i with x_i+ i0 = (x_i,0). Remember the complexification uses complex scalars.
• for 10, replace start of hint with: "Assume A ε M is such that some entry is non-zero. Make it 1, by multiplying A on the left by an appropriate matrix. Then show ..." Consider the effect of left and right multiplication of a matrix A by a standard basis vector E_ij described in example 10.
• Solutions

1.6: 2,4,5,6,8-10

• Due 10/11
• Solutions
  

1.7: 1-3,7,9
1.8: 1-3,5,11,13

• Due 10/18
• Solutions

1.9: 1-4
1.10: 1-6

• Due 10/29
• Solutions (section 9)
• Solutions (section 10)

1.11: 1,4,6,8
1.12: 2,4,8,9,10

• Due 11/8
• Solutions (section 11)
• Solutions (section 12)

Chapter 2

2.3: 1ab,2ab,3a,4ab,13,16,21

• Due 11/16
• Solutions

2.4: 1,4,6,7,8

• Due 11/23
• Solutions

2.5: 1ab,2ab,3a,4ab,8,13,15,18,19

• Due 12/8
• Most of the work for 1-4 was already done in section 3 HW
• Solutions