Linear Algebra Cheat Sheet - Excerpt From the No Bullshit Guide to Linear Algebra

A linear algebra cheat sheet is a quick reference guide that provides formulas, definitions, and concepts related to linear algebra. It is commonly used by students and professionals to quickly access important information while studying or working in the field of linear algebra.

FAQ

Q: What is linear algebra?
A: Linear algebra is a branch of mathematics that deals with vector spaces and linear mappings between them.

Q: What are vectors?
A: Vectors are mathematical objects that have both magnitude and direction.

Q: What are matrices?
A: Matrices are rectangular arrays of numbers that represent linear transformations or systems of linear equations.

Q: What is a determinant?
A: A determinant is a scalar value that can be computed from the elements of a square matrix and provides important information about the matrix.

Q: What is the rank of a matrix?
A: The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix.

Q: What is an eigenvector?
A: An eigenvector of a square matrix is a non-zero vector that only changes by a scalar factor when multiplied by the matrix.

Q: What is a eigenvalue?
A: An eigenvalue of a square matrix is a scalar value that represents how the corresponding eigenvector is scaled by the matrix.

Q: What is a diagonalizable matrix?
A: A diagonalizable matrix is a square matrix that can be transformed into a diagonal matrix by similarity transformation.

Q: What is a singular value decomposition?
A: Singular value decomposition is a factorization of a matrix into three matrices, which can provide valuable insights into the properties of the matrix.

Q: What is the dot product of two vectors?
A: The dot product of two vectors is a scalar value obtained by multiplying the corresponding components of the vectors and summing them.