The GATE Grind

GATE Mathematical Physics: matrices: similarity transformations, diagonalization, eigenvalues and eigen vectors – Previous Year Questions

3 GATE previous year questions on matrices: similarity transformations, diagonalization, eigenvalues and eigen vectors (Mathematical Physics, Physics) with answers and explanations, from every paper.

  1. GATE 2022 PH Q13 (1 mark, Multiple choice) – What is the maximum number of free independent real parameters specifying an n-dimensional orthogonal matrix?
  2. GATE 2023 PH Q26 (1 mark, Multiple choice) – A 44 matrix M satisfies M=-M and M4=1. Which is the correct eigenvalue set?
  3. GATE 2024 PH Q43 (2 marks, Multiple select) – Consider P=pmatrix1&2\\0&1pmatrix, Q=pmatrix1&0\\0&1pmatrix. Which statement(s) is/are true?