Linear algebra symbols

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Across
  1. 3. a scalar value that is a function of the entries of a square matrix.
  2. 4. an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space
  3. 6. to represent multiplication
  4. 7. dim(U)
  5. 8. A A^(-1)= I
  6. 10. (x, y)
Down
  1. 1. square matrix having the property that each pair of elements in the ith row and jth column and in the jth row and ith column are conjugate complex numbers
  2. 2. to move (a term) from one side of an equation to the other with a corresponding reversal in sign.
  3. 5. denoting the Euclidean norm. This is just the length of the vector
  4. 9. a binary operation on two vectors in a three-dimensional oriented Euclidean vector space, and is denoted by the symbol \times