Elijah's Linear Algebra Crossword

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Across
  1. 4. The ____of a matrix A is denoted det(A)
  2. 5. The ___ of a matrix is found by interchanging its rows into columns or columns into rows.
  3. 7. A real number is the ___ product of the lengths of two vectors and the cosine of the angle between them.
  4. 9. The complex ___ of a matrix interchanges the row and column index for each element, reflecting the elements across the main diagonal.
  5. 10. The ___ is the maximum number of its linearly independent column vectors (or row vectors).
Down
  1. 1. A matrix is always inside square ___.
  2. 2. The ___ of the matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity.
  3. 3. The ___ product of two real vectors in three dimensions is itself a vector at right angles to both the original vectors.
  4. 6. A 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.
  5. 8. The ___ of a matrix is the number of rows by the number of columns. If a matrix has rows and b columns, it is an a×b matrix.