A matrix whose determinant does not equal 0

Matrix that transforms between two basis.

The scalar λ such that:
Ax=λx

A matrix where all entries to the left of the main diagonal are 0.

(P^-1)(A)(P)

Determinant of the submatrix that remains after the i-th row and j-th column are deleted.

Number of vectors in a vector space V

det(λI-A)

Ax only has the trivial solution
The reduced row echelon form of A is I

Determinant, Rank, Nullity, Trace, Eigenvalues

The sum of the entries of an entire row or column multiplied by their corresponding cofactors.

The standard unit vectors that span Rn

Null space of matrix (λI-A)

(B^-1)(A^-1)

B=(P^-1)AP

The determinant that results when two rows or columns of A are interchanged

The only coefficients that satisfy
kv1+kv2+...+kvn
is 0

λ=a11
λ=a22
λ=a33
...
λ=ann

aA+bB+cC+...

A is nxn and has n linearly independent eigenvectors

If Ax = b is a system of n linear equations in n unknowns such that det(A) not equal to 0, then
the system has a unique solution. This solution is
x1 = det(A1)/det(A) , x2 = det(A2)/det(A) ,..., xn = det(An)/det(A)
where Aj is the matrix obtained by replacing the entries in the j th column of A by the
entries in the matrix b

A vector space W under the addition and scalar multiplication defined on space V

A=[3 0]
[ 8 -1]
[1]
[2]

The matrix that results from interchanging the rows and columns

D^7