Matrix Definitions

Question 1

What makes two matrices equal? (Definition: Equality)

Answer 1

Two matrices A and B are equal if they have the same order and their entries are all equal.

Question 2

What is a null matrix?

Answer 2

A matrix where all the entries are zero. Denoted by O

Question 3

What is a square matrix?

Answer 3

A matrix with the same number of rows and columns.

Question 4

What is a diagonal matrix?

Answer 4

An n x n matrix if, when i != j, A[i, j] = 0. NOTE: must also have at least one diagonal entry not equal 0.

Question 5

What is an identity matrix?

Answer 5

A diagonal matrix where all the diagonal entries are equal to 1. Denoted I subscript n for an n x n identity matrix.

Question 6

How do you transpose a matrix?

Answer 6

For every A[i, j] in a matrix, the entries of A ^ T will be [j, i] (so they flip). If A is a m x n matrix, then the transpose of A will be n x m.

Question 7

What is a symmetric matrix?

Answer 7

A matrix A that is equal to the transpose of A. A^T = A

Question 8

What is a skew symmetric matrix?

Answer 8

An n x n square matrix is skew if its transpose is equal to itself but negative. A^T = -A

Question 9

What is a scalar matrix?

Answer 9

A diagonal matrix with all the diagonal entries being equal