Matrix operations, matrix types, and basic matrix algebra from a college linear algebra course.
35 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a matrix?
- A rectangular array of numbers arranged in rows and columns.
- In matrix notation, what does a_ij represent?
- The element in the i-th row and j-th column of matrix A.
- What does it mean when a matrix has dimensions m by n?
- The matrix has m rows and n columns.
- What is a square matrix?
- A matrix with the same number of rows and columns, where m equals n.
- What is a row vector?
- A matrix with exactly one row, with dimensions 1 by n.
- What is a column vector?
- A matrix with exactly one column, with dimensions m by 1.
- What is the zero matrix?
- A matrix where every element equals zero.
- What is the identity matrix I_n?
- An n by n matrix with ones on the main diagonal and zeros everywhere else.
- What is a diagonal matrix?
- A square matrix with non-zero elements only on the main diagonal.
- What is an upper triangular matrix?
- A square matrix where all entries below the main diagonal are zero.
- What is a lower triangular matrix?
- A square matrix where all entries above the main diagonal are zero.
- When are two matrices equal?
- When they have the same dimensions and all corresponding elements are equal.
- What does it mean to multiply a matrix A by a scalar c?
- Multiply every element of A by c.
- What condition must be met to add two matrices?
- The matrices must have the same dimensions.
- How do you add two matrices A and B?
- Add corresponding elements: (A + B)_ij = a_ij + b_ij.