Matrices

2. Precisely specified and understood without ambiguity.
5. A system of equations with more equations than unknowns.
6. A set of vectors that are not expressible as linear combinations of each other.
9. To multiply across fractions or ratios, typically in solving proportions.
11. Having no defined limit or boundary, often expandable.
14. An element in a ring that, when multiplied by another non-zero element, gives zero.
18. A relationship that is not linear, i.e., does not form a straight line on a graph.
19. The signed minor of an element in a matrix, used in determinant expansion.
21. A quantity or term that is not equal to zero.
22. A matrix that is equal to the negative of its transpose.
25. A vector that changes only by a scalar factor when a linear transformation is applied to it.
27. A flat affine subspace of one dimension less than its ambient space.
29. An angle of 90 degrees, forming perpendicular lines or planes.
30. Involving more than one variable, commonly in functions or equations.

1. A system of equations with fewer equations than unknowns.
3. An operator that is equal to its own adjoint or Hermitian conjugate.
4. A smaller field contained within a larger mathematical structure.
7. A value that is either zero or positive, having no negative component.
8. Involving three dimensions, such as length, width, and depth.
10. Half of a circle, bounded by a diameter and the associated arc.
12. Existing in or involving two dimensions, such as length and width.
13. A subset of a vector space that is closed under vector addition and scalar multiplication.
15. A function that is linear in each of two variables independently.
16. A matrix where all eigenvalues are non-negative, though some may be zero.
17. Two numbers with no common factor other than 1.
20. A matrix with four rows and four columns.
23. An operation on two vectors in three-dimensional space resulting in a vector perpendicular to both.
24. Having a single value for each element in a specified domain.
26. A matrix with all entries equal to zero.
28. A set that can be well-ordered, meaning every subset has a least element.