Math Crossword

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Across
  1. 5. I capture changes when maps transform, Describing shifts in a linear form. What am I, this matrix wise, That shows how functions alter their guise?
  2. 7. In regions where my values smooth, I balance out with no sudden move. With no sources or sinks in sight, What am I, this steady light?
  3. 9. In spaces deep, I take my place, Measuring sets with subtle grace. Beyond the simple line and square, I find the size of shapes most rare.
  4. 10. I strike at a point with infinite might, Zero elsewhere, yet I hold tight. In integrals, I play my role, What am I, this concentrated whole?
  5. 11. In a world where points must part, I ensure that distance charts. Separation’s my guiding law, What am I, this distance saw?
  6. 13. I shift the time to s's embrace, Turning functions in a new space. From time to frequency, I reveal, What am I, this transforming deal?
  7. 15. In spaces curved, I lay my claim, Locally flat, yet never the same. A patchwork quilt, in math’s grand game, What am I, in topology’s name?
  8. 16. When I’m found, the matrix stays the same, A scalar that doesn’t change the game. What am I, this value key, That scales but leaves the vectors free?
  9. 17. In complex realms, I smoothly glide, My form unchanged on every side. A gentle flow without a break, What am I, in math’s deep wake?
Down
  1. 1. I map smooth paths from place to place, Preserving structure with gentle grace. Invertible and smooth, I fit just right, What am I, this seamless flight?
  2. 2. I’m born of matrices, a space I span, A vector space where norms do stand. With inner product, I find the norm, A metric space, where distances conform.
  3. 3. Complete normed vector space, I stand, Infinite dimensions, I command. Functional analysis, at hand, What am I, in this mathematical land?
  4. 4. I preserve the length and angle, too, A transformation, strong and true. In quantum realms, I play a part, Preserving states with all my heart.
  5. 6. I map your function to a new domain, Where slopes and curves take their own reign. A change of view, from one to two, What am I, this clever switch?
  6. 8. A whisper from a source unseen, I guide the path in fields between. From point to point, I bear the trace, Solving problems through empty space.
  7. 12. I track the symmetries in polynomial roots, Unraveling their hidden, abstract routes. What am I, this group of change, That captures the symmetry range?
  8. 14. In probability’s realm, I organize the space,With sets that form a measurable base. What am I, this algebraic array, That structures sets in a probabilistic way?