Linear Algebra Crossword

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