Vectors, matrices, eigenvalues, and vector space concepts from an introductory college linear algebra course.
40 cards · basic cards · AI-written, checked twice. Edit anything.
- What is a vector?
- An ordered list of numbers (or scalars) arranged in a specific sequence.
- What does it mean for two vectors to be parallel?
- One vector is a scalar multiple of the other.
- Define the dot product of two vectors.
- The sum of the products of their corresponding components.
- What is the norm (or length) of a vector?
- The square root of the sum of the squares of its components.
- Define orthogonal vectors.
- Vectors whose dot product is zero.
- What is a matrix?
- A rectangular array of numbers organized in rows and columns.
- What is the transpose of a matrix?
- The matrix obtained by swapping its rows and columns.
- When can two matrices be multiplied together?
- When the number of columns in the first equals the number of rows in the second.
- Define the identity matrix.
- A square matrix with ones on the main diagonal and zeros elsewhere.
- What is the determinant?
- A scalar value computed from a square matrix that encodes scaling and orientation properties.
- What does a zero determinant indicate about a matrix?
- The matrix is singular (non-invertible).
- What is an invertible matrix?
- A square matrix that has a multiplicative inverse (A * A inverse = I).
- Define an eigenvalue.
- A scalar lambda such that Av = lambda*v for some non-zero vector v.
- Define an eigenvector.
- A non-zero vector v such that Av = lambda*v for some scalar lambda.
- What is an eigenspace?
- The set of all eigenvectors corresponding to a particular eigenvalue, plus the zero vector.