Determinant
A determinant is a scalar computed from a square matrix that characterizes properties such as invertibility and signed volume scaling.
Geometry for Programmers
A determinant is a scalar computed from a square matrix that encodes algebraic properties such as invertibility and signed volume scaling.
- How it is used
- Uses determinants to connect triple products and box products with signed geometric volume.
- How deep it goes
- Explains orientation and volume, demonstrates SymPy through 4D, and defers alternative large-dimension algorithms.
- Examples
- Uses unit vectors, 2D through 4D symbolic matrices, and SymPy determinant listings.
- What you can do after
- Apply via SymPy to compute small-dimensional symbolic determinants and recognize when numeric solvers are more suitable.
Math and Architectures of Deep Learning
A scalar quantity computed from a square matrix, appearing here in the Wishart density via matrix absolute-value notation.
- How it is used
- Uses determinant values to assess matrix invertibility, exact solvability, and numerical conditioning in linear systems.
- How deep it goes
- Explains dependence, singularity, inversion, and instability through a 2×2 example, but defers general determinant computation rules.
- Examples
- Uses duplicated equations and the calculation 2 × 1 − 1 × 2 = 0 to illustrate a singular coefficient matrix.
- What you can do after
- Evaluate whether a square matrix is invertible and recognize when its associated system is singular or numerically unstable.
Read how Math and Architectures of Deep Learning explains determinant →
Related concepts
- vector-to-vector productused by · A vector-to-vector product is an operation combining two vectors according to a defined rule to produce a scalar or another vector.
- triple productequivalent to · The triple product is the scalar obtained by taking the dot product of one vector with the cross product of two other vectors, equal to the signed volume of their parallelepiped.
- Kullback–Leibler divergenceused by · Kullback–Leibler divergence is a nonnegative, directed measure of the information lost when one probability distribution approximates another, computed as an expected log ratio under the first distribution.
- matrix inverseuses · A matrix inverse is a matrix that, when it exists, multiplies with a square matrix to produce the identity matrix.
- matrix inversioncontrasts with · Matrix inversion is the operation of computing a matrix that, when multiplied by a given invertible matrix, produces the identity matrix.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.