### 1. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 25-1.1 (to Problem 25-1 “Moore Penrose inverse of a skew-symmetric matrix” proposed by Jürgen Groβ, Sven-Oliver Troschke & Götz Trenkler). *IMAGE* **26** (2001) 2.

### 2. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 25-4.1 (to Problem 25-4 “Two rank equalities associated with blocks of an orthogonal projector” proposed by Yongge Tian). *IMAGE* **26** (2001) 6-7.

### 3. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 25-5.1 (to Problem 25-5 “Three inequalities involving Moore—Penrose inverses” proposed by Yongge Tian). *IMAGE* **26** (2001) 9-10.

### 4. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 25-6.1 (to Problem 25-6 “Generalized inverse of a matrix product” proposed by Yongge Tian). *IMAGE* **26** (2001) 10-11.

### 5. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 26-4.1 (to Problem 26-4 “Commutativity of EP matrices” proposed by Yongge Tian). *IMAGE* **27** (2001) 30.

### 6. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 26-5.1 (to Problem 26-5 “Convex matrix inequalities” proposed by Bao-Xue Zhang). *IMAGE* **27** (2001) 33-34.

### 7. Jerzy K. Baksalary & Oskar Maria Baksalary

Problem 29-1 “A condition for an EP matrix to be Hermitian”. *IMAGE* **29** (2002) 36.

### 8. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 27-2.1 (to Problem 27-2 “Specific generalized inverses” proposed by Jürgen Groβ and Götz Trenkler). *IMAGE* **28** (2002) 29.

### 9. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 28-5.1 (to Problem 28-5 “A range equality for Moore—Penrose inverses” proposed by Yongge Tian). *IMAGE* **29** (2002) 28-29.

### 10. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 28-7.2 (to Problem 28-7 “Partial isometry and idempotent matrices” proposed by Götz Trenkler). *IMAGE* **29** (2002) 31.

### 11. Oskar Maria Baksalary

Solution 28-2.2 (to Problem 28-2 “Linear combinations of imaginary units” proposed by Richard William Farebrother). *IMAGE* **29** (2002) 26. Correction from the author: *IMAGE* **30** (2003) 21.

### 12. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 29-5.1 (to Problem 29-5 “Product of two Hermitian nonnegative definite matrices” proposed by Jürgen Groβ). *IMAGE* **30** (2003) 24-25.

### 13. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 30-5.1 (to Problem 30-5 “A range equality for the difference of orthogonal projectors” proposed by Yongge Tian). *IMAGE* **31** (2003) 36-37.

### 14. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 30-6.1 (to Problem 30-6 “A matrix related to an idempotent matrix” proposed by Götz Trenkler). *IMAGE* **31** (2003) 39.

### 15. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 30-7.1 (to Problem 30-7 “A condition for an idempotent matrix to be Hermitian” proposed by Götz Trenkler). *IMAGE* **31** (2003) 41.

### 16. Jerzy K. Baksalary, Oskar Maria Baksalary & Xiaoji Liu

Problem 30-1 “Star partial ordering, left-star partial ordering, and commutativity”. *IMAGE* **30** (2003) 36.

### 17. Jerzy K. Baksalary, Oskar Maria Baksalary & Xiaoji Liu

Solution 30-1.1 (to Problem 30-1 “Star partial ordering, left-star partial ordering, and commutativity” proposed by Jerzy K. Baksalary, Oskar Maria Baksalary & Xiaoji Liu). *IMAGE* **31** (2003) 30-31.

### 18. Oskar Maria Baksalary & Katarzyna Chyli??ska

Solution 29-10.2 (to Problem 29-10 ??Equivalence of three reverse-order laws? proposed by Yongge Tian). *IMAGE ***30** (2003) 31-32.

### 19. William F. Trench, Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 29-1.2 (to Problem 29-1 “A condition for an EP matrix to be Hermitian” proposed by Jerzy K. Baksalary & Oskar Maria Baksalary). *IMAGE* **30** (2003) 22.

### 20. Jerzy K. Baksalary & Oskar Maria Baksalary

Solution 31-7.1 (to Problem 31-1 “On the product of orthogonal projectors” proposed by Götz Trenkler). *IMAGE* **32** (2004) 30-31.

### 21. Jerzy K. Baksalary, Oskar Maria Baksalary & Xiaoji Liu

Solution 31-2.1 (to Problem 31-2 “Matrices commuting with all nilpotent matrices” proposed by Henry Ricardo). *IMAGE* **32** (2004) 21-22.

### 22. Oskar Maria Baksalary

Solution 31-8.1 (to Problem 31-8 “Eigenvalues and eigenvectors of a particular tridiagonal matrix” proposed by Fuzhen Zhang). *IMAGE* **32** (2004) 37.

### 23. Oskar Maria Baksalary

Solution 33-6.1 (to Problem 33-6 “Projectors and similarity” proposed by Götz Trenkler). *IMAGE* **34** (2005) 35.

### 24. Oskar Maria Baksalary

Solution 34-9.2 (to Problem 34-9 “A sum property for the Moore—Penrose inverse of EP matrices” proposed by Götz Trenkler). *IMAGE* **35** (2005) 41.

### 25. Oskar Maria Baksalary & Xiaoji Liu

Solution 34-8.1 (to Problem 34-8 “A property for the sum of a matrix *A* and its Moore—Penrose inverse A^{†}” proposed by Götz Trenkler). *IMAGE ***35** (2005) 39-40.

### 26. Oskar Maria Baksalary & Xiaoji Liu

Solution 34-10.1 (to Problem 34-10 “On the product of orthogonal projectors” proposed by Götz Trenkler). *IMAGE* **35** (2005) 42.

### 27. Oskar Maria Baksalary & Xiaoji Liu

Solution 35-7.1 (to Problem 35-7 “A characterization of oblique projectors” proposed by Götz Trenkler). *IMAGE* **36 **(2006) 31.

### 28. Oskar Maria Baksalary & Xiaoji Liu

Solution 35-8.1 (to Problem 35-8 “A characterization of a particular class of square complex matrices” proposed by Götz Trenkler). *IMAGE* **36** (2006) 32-33.

### 29. Oskar Maria Baksalary & G??tz Trenkler

Problem 37-1 “Another property for the sum of a matrix *A* and its Moore—Penrose inverse A^{†}”. *IMAGE* **37** (2006) 32.

### 30. Oskar Maria Baksalary & G??tz Trenkler

Problem 37-2 ??Rank of a generalized projector?. *IMAGE* **37** (2006) 32.

### 31. Oskar Maria Baksalary & G??tz Trenkler

Problem 37-3 ??Rank of a nonnegative definite matrix?. *IMAGE* **37** (2006) 32.

### 32. Oskar Maria Baksalary & G??tz Trenkler

Solution 37-1.1 (to Problem 37-1 ??Another property for the sum of a matrix *A* and its Moore??Penrose inverse A^{?}? proposed by Oskar Maria Baksalary & G??tz Trenkler). *IMAGE* **39** (2007) 23-24.

### 33. Oskar Maria Baksalary & G??tz Trenkler

Solution 37-2.1 (to Problem 37-2 ??Rank of a generalized projector? proposed by Oskar Maria Baksalary & G??tz Trenkler). *IMAGE* **39** (2007) 25-26.

### 34. Oskar Maria Baksalary & G??tz Trenkler

Solution 37-3.1 (to Problem 37-3 ??Rank of a nonnegative definite matrix? proposed by Oskar Maria Baksalary & G??tz Trenkler). *IMAGE* **39** (2007) 27.

### 35. Oskar Maria Baksalary & G??tz Trenkler

Solution 37-6.1 (to Problem 37-6 ??Characterization of EP-ness? proposed by G??tz Trenkler). *IMAGE ***39** (2007) 30.

### 36. Oskar Maria Baksalary & G??tz Trenkler

Problem 11379. *The* *American Mathematical Monthly ***115** (2008) 664.

### 37. Oskar Maria Baksalary & G??tz Trenkler

Problem 11387. *The American Mathematical Monthly ***115** (2008) 758.

### 38. Oskar Maria Baksalary & G??tz Trenkler

Problem 41-1 ??A lower bound for the rank of A + A*?. *IMAGE* **41** (2008) 42.

### 39. Oskar Maria Baksalary & G??tz Trenkler

Problem 41-2 ??An inequality involving a semi-inner product?.* IMAGE* **41** (2008) 42.

### 40. Oskar Maria Baksalary & G??tz Trenkler

Problem 41-3 ??A Property of the Range of Generalized and Hypergeneralized Projectors?. *IMAGE* **41** (2008) 43.

### 41. Oskar Maria Baksalary & G??tz Trenkler

Problem 41-12 ??An inequality involving a product of two orthogonal projectors?. *IMAGE* **41** (2008) 44.

### 42. Oskar Maria Baksalary, Roger Horn & G??tz Trenkler

Problem 41-13 ??Range Additivity of *A* and *A**?. IMAGE **41** (2008) 43.

### 43. Oskar Maria Baksalary & G??tz Trenkler

Problem 882 *??*An inequality with positive definite matrices*?. The College Mathematics Journal* **39** (2008) 307-308.

### 44. Oskar Maria Baksalary & G??tz Trenkler

Solution 39-5.1 (to Problem 39-5 “Two commutativity equalities for the regularized Tikhonov inverse” proposed by Yongge Tian). *IMAGE ***41** (2008) 37-38.

### 45. Oskar Maria Baksalary & G??tz Trenkler

Solution 39-6.1 (to Problem 39-6 “Two equalities for the Moore—Penrose inverse of a row block matrix” proposed by Yongge Tian). *IMAGE* **41** (2008) 40.

### 46. Oskar Maria Baksalary & G??tz Trenkler

Problem 42-1 “Square root of a product of two orthogonal projectors”. *IMAGE* **41** (2009) 40.

### 47. Oskar Maria Baksalary & G??tz Trenkler

Solution 41-1 (to Problem 41-1 “A lower bound for the rank of *A* + *A**” proposed by Oskar Maria Baksalary & Götz Trenkler).* IMAGE ***42** (2009) 27-28.

### 48. Oskar Maria Baksalary & G??tz Trenkler

Solution 42-2 (to Problem 41-2 “An inequality involving a semi-inner product” proposed by Oskar Maria Baksalary & Götz Trenkler).* IMAGE ***42** (2009) 28.

### 49. Oskar Maria Baksalary, Roger Horn & G??tz Trenkler

Solution 41-13 (to Problem 41-13 “Range additivity of *A* and *A**” proposed by Oskar Maria Baksalary, Roger Horn & Götz Trenkler).* IMAGE ***42** (2009) 37.

### 50. Oskar Maria Baksalary & G??tz Trenkler

Solution 42-2.1 (to Problem 42-2 “Properties of a certain matrix product” proposed by Richard William Farebrother). *IMAGE* **43** (2009) 37-38.

### 51. Oskar Maria Baksalary & G??tz Trenkler

Problem 43-1 “Characterization of EP matrices”. *IMAGE* **43** (2009) 44.

### 52. Oskar Maria Baksalary & G??tz Trenkler

Problem 44-1 “Constrained characterization of hermitianness”. *IMAGE* **44** (2010) 44.

### 53. Oskar Maria Baksalary & G??tz Trenkler

Problem 45-1 “Column space counterparts of the known conditions for orthogonal projectors”. *IMAGE* **45** (2010) 48.

### 54. Oskar Maria Baksalary & G??tz Trenkler

Solution 44-1.1 (to Problem 44-1 “Constrained characterization of hermitianness” proposed by Oskar Maria Baksalary & Götz Trenkler). *IMAGE* **45** (2010) 40.

### 55. Oskar Maria Baksalary & G??tz Trenkler

Problem 95.D. *The Mathematical Gazette* **95** (2011) 133.

### 56. Oskar Maria Baksalary & G??tz Trenkler

Problem 46-1 “Space decomposition in terms of column and null spaces”. *IMAGE* **46** (2011) 48.

### 57. Oskar Maria Baksalary & G??tz Trenkler

Solution 45-1.1 (to Problem 45-1 “Column space counterparts of the known
conditions for orthogonal projectors” proposed by Oskar Maria Baksalary
& Götz Trenkler). *IMAGE* **46** (2011) 39-40.

### 58. Oskar Maria Baksalary & G??tz Trenkler

Problem 47-2 “Another characterization of normality”. *IMAGE*** 47** (2011) 40.

### 59. Oskar Maria Baksalary & G??tz Trenkler

Solution (to Problem 11466 proposed by Yongge Tian). *The American Mathematical Monthly* **119** (2012) 162-163.

### 60. Oskar Maria Baksalary & G??tz Trenkler

Problem 48-1 “Reverse Order Law for the Core Inverse”. *IMAGE* **48** (2012) 40.

### 61. Oskar Maria Baksalary & G??tz Trenkler

Problem 1904. *Mathematics Magazine* **85** (2012) 296.

### 62. Oskar Maria Baksalary & G??tz Trenkler

Problem 49-1 “Generalized eigenvalues of a pair of orthogonal projectors”. *IMAGE* **49** (2012) 52.

### 63. Oskar Maria Baksalary & G??tz Trenkler

Solution 48-2.1 (to Problem 48-2 “Minimality for the nonzero singular values of an idempotent matrix“ proposed by Johanns De Andrade Bezerra). *IMAGE* **49** (2012) 47.

### 64. Oskar Maria Baksalary & G??tz Trenkler

Aufgabe 1312. *Elemente der Mathematik ***68** (2013) 39.

### 65. Oskar Maria Baksalary & G??tz Trenkler

Problem 50-2 “Range-hermitianness of certain functions of projectors”. *IMAGE ***50** (2013) 44.

### 66. Oskar Maria Baksalary & G??tz Trenkler

Solution 50-2.2 (to Problem 50-2 ''Range-hermitianness of certain
functions of projectors'' proposed by Oskar Maria Baksalary & Götz
Trenkler).
*IMAGE* **51** (2013) 43.

### 67. Oskar Maria Baksalary & G??tz Trenkler

Problem 52-2 “Numerical range of a skew-symmetric matrix”. *IMAGE ***52** (2014) 48.