Linear Algebra Crossword

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Across
  1. 5. Function from one vector space to another that respects the underlying structure of each vector space (2 words)
  2. 9. operator which flips a matrix over its diagonal
  3. 12. two vectors are this if one can be changed to the other by a sequence of elementary row operations (2 words)
  4. 13. set of all linear combinations of a set of vectors
  5. 14. vectors are this if there is a nontrivial linear combination of the vectors that equals the zero vector (2 words)
  6. 15. Form a matrix can be in after Gaussian elimination (2 words)
  7. 18. matrix in which the entries outside the main diagonal are all zero
  8. 19. the dimension of the vector space spanned by a matrix's columns
  9. 20. Nonempty set of vectors closed under two operations and that is subject to ten axioms (2 words)
  10. 21. Two or more equations that share variables (3 words)
Down
  1. 1. Scalar value that is a function of the entries of a square matrix
  2. 2. a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros
  3. 3. Rectangular array of numbers, symbols, or expressions
  4. 4. The number of vectors in a basis for a vector space
  5. 6. What two vectors are if their dot products is zero
  6. 7. Vector space that is a subset of some larger vector space
  7. 8. operations that allow one to transform a system of linear equations into an equivalent system (2 words)
  8. 10. Word for if a matrix has a nonzero determinant
  9. 11. vector space generated by linear combinations of the matrix's row vectors (2 words)
  10. 16. the span of a matrix's column vectors (2 words)
  11. 17. Non-zero vector that can be changed at most by its scalar factor after the application of linear transformations