Linear Systems & Matrices
This type of square matrix represents a system with exactly one solution.
What is nonsingular?
This number represents the size of a vector space.
What is dimension?
The inner product of this object with itself is 1.
What is a unit vector?
These special numbers are named after the German word for proper.
What are eigenvalues?
This award is given to exceptional mathematicians in their prime.
What is the Fields Medal?
This kind of encryption is also a type of matrix with a relationship to its transpose.
What is symmetric?
All vector spaces have this property often sought at the end of a relationship.
What is closure?
This is the vector in a subspace W that is closest to a given vector v.
What is the projection (of v onto W)?
An eigenvector x of a linear transformation L and its output L(x) are this (in relation to each other).
What is parallel?
This type of argument involves assuming something false.
What is proof by contradiction?
This object's volume is given by the determinant of the matrix whose rows span it.
What is a parallelepiped?
Two linearly dependent vectors in R2 have this geometric property (in relation to each other).
What is parallel(ism)?
Any vector in a vector space V can be uniquely written as the sum of an element in a subspace W and an element in this set.
What is Wperp?
This physical reaction to dim lighting is also a type of linear transformation.
What is dilation?
This mathematician proved a theorem that was scribbled in the margins.
Who is Andrew Wiles?
This type of matrix with an easy-to-compute determinant resembles an unresolved romantic situation.
What is triangular?
An orthogonal spanning set of nonzero vectors in a vector space is this.
What is a basis?
Any vector in the row space of a matrix A and any vector in the null space of A are this (in relation to each other).
What is orthogonal?
This is the rank of an nxn matrix that has only nonzero eigenvalues.
What is n?
This was Euler's name for what we now know as the field of graph theory.
What is the geometry of position?
This is the nullity of an nxn matrix with nonzero determinant.
What is zero?
The rows or columns of a singular matrix have this property.
What is linear dependence?
This is the orthogonal complement of the column space of a matrix A.
What is the null space of AT?
Jim Croce wrote a song about this type of linear transformation.
What is a (linear) operator?
What are Math, French, and Literary Arts?