Systems of Linear Equations and Matrices | Determinants | Euclidean Vector Spaces | General Vector Spaces | Eigenvalues and Eigenvectors |
---|---|---|---|---|
What is No?
This answers the question of whether AB=BA, given that A and B are both matrices.
|
What is n*n?
There are this many cofactors in an n*n matrix.
|
What is the norm?
The magnitude of vector V can also be called by this 4 letter word.
|
What is 10?
There are this many axioms to confirm that a set of objects is a vector space.
|
What is false?
True or false answers whether the eigenvalues of a matrix are solely determined by the main diagonal.
|
What is R^6?
The domain of a 5*6 matrix is this.
|
What is false?
Out of true and false, this is the correct answer to the statement that the sum of the determinants of two matrices is equal to the determinant of the sum of the matrices.
|
What is the cosine?
This trignometric function can be used to calculate the dot product of 2 vectors.
|
What is the zero subspace?
This subspace only has one vector in it.
|
What is 0?
This number can't be a eigenvalue for a matrix to be invertible.
|
What is when there's a sequence of elementary row operations that transforms one matrix to the other?
Two matrices are row equivalent when this condition is true.
|
What is 2?
Out of the 3 elementary row operations, this many change the determinant.
|
What is the normal?
The coefficients in the equation of the line 5(x-1) +4(y+3) are components of this vector that is orthogonal to the line.
|
What is if every vector in one span can be written as linear combinations of the vectors in the other, and vice versa?
Two spans are equal to each other if this is true.
|
What is det(λI − A) = 0?
This formula is called the characteristic equation of matrix A.
|
What is the trace?
This is the sum of the diagonal elements of a matrix.
|
What is the adjoint?
The transpose of the matrix of cofactors of matrix A is called this.
|
What is the Cauchy–Schwarz inequality?
This inequality desrcibes the statement where the magnitude of two multiplied vectors is less than the product of the two magnitudes of the individual vectors.
|
What is the Wronskian?
If this determinant is 0, the set of differentiable functions is linearly dependent.
|
What is a similarity invariant?
This is a property that is preserved by a similarity transformation.
|
What is when they commute with each other?
This condition needs to met for the product of 2 symetric matrices to be symmetric.
|
What is (k^n)(x) OR (k^n)(det A)?
If A is an n*n matrix, and determinant A= x, det(kA) is equal to this.
|
What is the parallelpiped?
The scalar addition of 3 vectors u+v+w composes the digonal of this figure.
|
What is the column space of A?
This is the orthogonal complement to the null space of the transpose of A.
|
What is true?
Either true or false is the answer to the statement that tr(A)= tr(P^-1 AP)
|