linear algebra

3. a constant commonly used to represent eigenvalues
5. a matrix which will transform any vector onto itself
6. the name of a common input-output economic problem
9. the closest position in one subspace to a vector
13. the length of the vector between the solution of best fit and the actual solution
14. the class about lines
16. a factorization comprised of orthonormal eigenvectors and a diagonalized matrix of eigenvalues
17. the set of vectors obtainable by a linear combination of a set of vectors
18. a quantity that has both magnitude and direction, often represented as an arrow
19. when the matrix has a unique output vector for each unique input vector

1. the set of vectors closed under addition and scalar multiplication of a set of vectors
2. the sum of the elements on the matrix's diagonal
4. the state of having a cross product of 0
7. a word describing the polynomial by which eigenvalues can be found
8. a vector which is a scalar multiple of itself after transformation
10. the scalar by which a vector could be multiplied after a linear transformation
11. the matrix which will transform another matrix onto the identity matrix
12. the type of chain made up of stochastic matrices
13. the number of dimensions in the column space of a matrix
14. the same for a factorization in which part of a matrix is made upper triangular
15. a word describing coordinates by which a vector could be translated
17. any set of vectors
20. a form in which coefficients are placed adjacent to the output they must obtain
21. when the matrix can transform vectors to any position in its output dimension