The Linear Logo

Dr. Mark V. Sapir

List of concepts and definitions

  1. Linear equation
  2. Solution of a linear equation
  3. System of linear equations
  4. Solution of a system of linear equations
  5. A consistent system of equations
  6. General solution of a system of linear equations
  7. Operations on systems of linear equations
  8. Augmented matrix of a system of lin. equations
  9. Row operations on matrices
  10. Row-echelon form
  11. Leading 1 in a row echelon matrix
  12. Reduced row-echelon form
  13. Leading unknown
  14. Free unknown
  15. Back-substitution
  16. Gauss-Jordan elimination procedure
  17. Homogenious system of lin. equations
  18. Size of a matrix
  19. Entry of a matrix
  20. Row-vector
  21. Column-vector
  22. Square matrix
  23. Scalar
  24. Equality of matrices
  25. Sum of matrices
  26. Multiplying a matrix by a scalar
  27. Product of a row-vecror and a column-vector
  28. Product of matrices
  29. Matrix of coefficients of a system of equations.
  30. Zero matrix
  31. Identity matrix
  32. Transpose of a matrix
  33. Trace of a matrix
  34. Invertible matrix
  35. Inverse of a matrix
  36. Elementary matrix
  37. The inverse of an elementary matrix
  38. Symmetric matrices
  39. Diagonal matrices
  40. Upper- and lowertriangular matrices
  41. Skew-symmetric matrices
  42. A transposition
  43. Determinant of a square matrix
  44. Sign of a permutation
  45. An inversion in a permutation.
  46. Even and odd permutations.
  47. Cofactor of entry aij.
  48. Minor of entry aij.
  49. Cofactor expansion along a row (column)
  50. The adjoint of a matrix
  51. Cramer's rule
  52. Algebraic system
  53. n-space
  54. n-vector
  55. Coordinates of an n-vector
  56. Vector space
  57. Triangle
  58. Dot product (Euclidean inner product) of n-vectors
  59. Dot product (inner product) of functions
  60. Properties of dot product
  61. Euclidean vector space
  62. Norm of a vector
  63. Distance between two vectors
  64. Orthogonal vectors
  65. Linear transformation from Rn to Rm
  66. Linear operator on Rn
  67. Standard matrix of a linear transformation
  68. The product of linear transformations
  69. The sum of linear transformations
  70. Injective maps
  71. Surjective maps
  72. General linear transformations
  73. General linear operator
  74. Null transformation
  75. Identity operator
  76. Subspace of a vector space.
  77. Kernel of a linear transformation
  78. Range of a linear transformation
  79. Linear combination of vectors
  80. Vector space spanned by a set of vectors
  81. The null space of a matrix
  82. Column space of a matrix
  83. Linearly independent sets of elements in a vector space.
  84. Linearly dependent sets of elements in a vector space.
  85. The Wronskian of a set of functions
  86. A basis of a vector space
  87. The dimension of a vector space
  88. Coordinates of a vector in a given basis
  89. Rank of a set of vectors
  90. Core of a set of vectors
  91. Orthogonal complement of a subspace
  92. Orthogonal basis
  93. Gram-Schmidt procedure
  94. Projection of a vector onto a subspace
  95. Normal component of a vector
  96. Distance from a vector to a set in a Euclidean vector space
  97. A least squares solution of a system of linear equations
  98. A transition matrix from one basis to another
  99. The matrix of a linear operator in a given basis
  100. Similar matrices
  101. Eigenvector and eigenvalue of a linear operator
  102. Eigenvector and eigenvalue of a matrix
  103. The characteristic polynomial of a matrix