Linear algebra symbols

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Across
  1. 3. A†
  2. 5. vector product
  3. 7. matrix tranpose.
  4. 9. [ ]
  5. 10. Symbol name of rank(A).
Down
  1. 1. | A |
  2. 2. meaning or definition of || x ||.
  3. 4. ⟨ x,y⟩
  4. 6. A -¹
  5. 8. scalar product.