Math 73: Final Project

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Across
  1. 2. The set of all solutions to the homogenous system Ax=0.
  2. 6. The length of a vector
  3. 8. The dimension of the eigenspace corresponding to a specific eigenvalue
  4. 11. The span of the rows of a matrix.
  5. 13. A set is _________ if each pair of vectors have a dot product of 0
  6. 16. If every vector in one vector space is an output for some vector in another vector space
  7. 18. A directed line segment that represents displacement.
  8. 19. The number of vectors in a basis for the vector space
  9. 21. The number of linearly independent rows or columns
  10. 22. A set of vectors such that every vector in the vector space can be expressed as a unique combination
  11. 23. 1. interchange rows 2. multiply a row by a nonzero constant 3. add multiples of a row to another
  12. 25. A type of inner product.
  13. 27. Set of all vectors in a subspace that are mapped by T to the 0 vector of another subspace
  14. 28. A subset of a vector space that falls under the same operations of addition and scalar multiplication
  15. 30. An array that can represent a system of equations.
  16. 31. A matrix that transforms a coordinate vector from one basis to another
  17. 33. An expression that represents a vector v as a scalar combination of vectors v1 through vk with scalars c1 through ck.
  18. 34. The factor by which areas or volumes are scaled by the matrix.
Down
  1. 1. If the matrix A is ____________ there exists an invertible matrix P such that P^-1AP=D
  2. 3. A scalar of a matrix such that there is a nonzero vector x where Ax=𝜆x.
  3. 4. The coefficients of the linear combination relative to a specific basis. They represent a specific vector
  4. 5. From a vector space V to a vector space W is a mapping T:V-->W
  5. 7. A collection of one or more linear equations.
  6. 9. When a transformation is one to one and onto
  7. 10. The system of equations is ____________ if the constant term in each equation is 0.
  8. 12. The ith column of matrix A becomes the ith row
  9. 13. If no two vectors of one vector space map to the same vector of another vector space
  10. 14. Matrix multiplication
  11. 15. The span of the columns of a matrix.
  12. 17. Number of times an eigenvalue appears
  13. 20. A set of vectors that are orthogonal to each other and are unit vectors
  14. 24. None of the vectors in the set can be expressed as a linear combination of any of the other vectors
  15. 26. The shadow that one vector casts onto another.
  16. 29. Matrix A is symmetric if A=A^T
  17. 32. Set of all vectors in a subspace that are images from another subspace under a transformation, which includes the 0 vector