Linear Algebra

What is a linear equation?

What is the magnitude (length or norm) of a vector?

What is the relationship between a vector’s magnitude and scalar multiplication?

What is the triangle inequality or the Cauchy Schwartz inequality?

How do you find the inner product (also called the dot product) of 2 vectors?

How do you find the angle between two vectors in two-space?

What is the additive identity in arithmetic and for matrices?

0 for arithmetic and zero matrix for matrices.

Zero matrix comes in all sizes and shapes.

What is the multiplicative identity in arithmetic and for matrices?

I in arithmetic and identify matrix for matrices.

Identity matrix comes in all sizes but is always square in shape.

Multiplying a matrix by its identity matrix is multiplicatively commutative.

What is commutativity?

It means you can reverse the order

When can matrix multiplication be commutative?

1) When multiplying a square matrix by its multiplicative identity

2) When multiplying by the inverse of the matrix (if one exists)

When are matrices said to be upper triangle or lower triangle?

A triangular matrix is square shaped.

Upper triangular: All elements BELOW the main triangle are zeros.

Lower triangular: All elements ABOVE the main diagonal are zeros.

What is a diagonal matrix?

One where all entire above and below the main diagonal are zeros + it is square in shape

When is a square matrix singular or non-singular?

A square matrix is non-singular if it has a multiplicative inverse.

A square matrix is singular if it doesn’t have a multiplicative inverse.

What is meant by matrix addition being associative?

(A + B) + C = A + (B + C)

What are the 5 multiplication properties for matrices?

A * B ≠ B * A

kA = Ak

(A * B) * C = A * (B * C)

(kA) * B = k(A * B)

(kl)A = k(lA)