Linear Algebra Crossword

4. operations that allow one to transform a system of linear equations into an equivalent system (2 words)
7. Scalar value that is a function of the entries of a square matrix
9. vectors are this if there is a nontrivial linear combination of the vectors that equals the zero vector (2 words)
11. set of all linear combinations of a set of vectors
12. The number of vectors in a basis for a vector space
13. matrix in which the entries outside the main diagonal are all zero
14. Form a matrix can be in after Gaussian elimination (2 words)
17. vector space generated by linear combinations of the matrix's row vectors (2 words)
18. a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros
19. two vectors are this if one can be changed to the other by a sequence of elementary row operations (2 words)
20. operator which flips a matrix over its diagonal

1. Nonempty set of vectors closed under two operations and that is subject to ten axioms (2 words)
2. What two vectors are if their dot products is zero
3. the dimension of the vector space spanned by a matrix's columns
5. Vector space that is a subset of some larger vector space
6. Non-zero vector that can be changed at most by its scalar factor after the application of linear transformations
8. Function from one vector space to another that respects the underlying structure of each vector space (2 words)
10. Word for if a matrix has a nonzero determinant
11. Two or more equations that share variables (3 words)
15. the span of a matrix's column vectors (2 words)
16. Rectangular array of numbers, symbols, or expressions