math

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Across
  1. 4. an element of a field, which is used to define a vector space, usually the field of real numbers
  2. 5. the process of uniting two or more numbers into one sum, represented by the symbol +.
  3. 7. the set of elements that a given function from one set to a second set maps into the identity of the second set.0
  4. 9. a non-zero element of a matrix selected by an algorithm
  5. 15. the act of changing the order of elements arranged in a particular order, as abc into acb, bac, etc., or of arranging a number of elements in groups made up of equal numbers of the elements in different orders, as a and b in ab and ba; a one-to-one transformation of a set with a finite number of elements.
  6. 16. the operation or process of finding the difference between two numbers or quantities, denoted by a minus sign
  7. 17. pertaining to an algebraic system in which all the elements of a group are powers of one element.
  8. 20. a scalar value that is a function of the entries of a square matrix.
  9. 21. A matrix with the same number of rows and columns, sometimes used to represent a linear transformation from a vector space to itself, such as reflection, rotation, or shearing.
  10. 22. straight line has one dimension, a parallelogram has two dimensions, and a parallelepiped has three dimensions.
Down
  1. 1. to interchange rows and columns.
  2. 2. a set of certain rows and columns of a given matrix.
  3. 3. defined so that its product with its transpose results in the identity matrix.
  4. 6. two matrices is defined if and only if the number of columns of the left matrix is the same as the number of rows of the right matrix
  5. 8. an expression or a proposition, often algebraic, asserting the equality of two quantities.
  6. 10. a straight line segment whose length is magnitude and whose orientation in space is direction
  7. 11. the product of the minor of a given element of a matrix times −1 raised to the power of the sum of the indices of the row and column crossed out in forming the minor.
  8. 12. The mathematical notion an abstraction of the process of making a geographical map.
  9. 13. a subspace of a vector space that has dimension one less than the dimension of the vector space.
  10. 14. a subset of a vector space which is itself a vector space
  11. 18. a mathematical method of calculation where the numbers to be added or subtracted are set out above one another in columns.
  12. 19. a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.