Frequently Asked Questions

• Q1: What is a matrix rank?
  A: The rank of a matrix is the maximum number of linearly independent rows or columns.
• Q2: How to calculate the rank of a matrix?
  A: Use row-reduction or determinant-based methods to find the rank.
• Q3: What is a full-rank matrix?
  A: A matrix is full-rank if its rank equals its smaller dimension.
• Q4: Can rank be larger than matrix dimensions?
  A: No, the rank cannot exceed the number of rows or columns.
• Q5: Is rank affected by matrix transposition?
  A: No, the rank remains the same after transposition.
• Q6: What is rank-deficient?
  A: A matrix is rank-deficient if its rank is less than its dimensions.
• Q7: How do singular matrices affect rank?
  A: Singular matrices have a rank less than their order.
• Q8: What is the rank of a zero matrix?
  A: The rank of a zero matrix is zero.
• Q9: What is a row-echelon form?
  A: It’s a simplified form used for calculating rank.
• Q10: Can rank be negative?
  A: No, rank is always a non-negative integer.