Rotation matrix
A rotation matrix is a square matrix representing a linear transformation that rotates vectors while preserving their lengths and angles.
Math and Architectures of Deep Learning
A matrix that represents a geometric rotation in this section, with orthogonal rotation matrices being length-preserving and invertible by transposition.
- How it is used
- Uses rotations to connect geometric transformations with matrix properties and machine-learning tools.
- How deep it goes
- Develops formulas, geometric properties, PyTorch checks, eigen-axes, and hyperellipse alignment without extending into later applications.
- Examples
- Demonstrates planar and axis-specific rotations, sequential 3D rotations, PyTorch assertions, and a 45-degree hyperellipse axis.
- What you can do after
- Apply it via PyTorch to construct rotations, transform vectors, verify orthogonality, reverse angles, and find hyperellipse axes.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI
A rotation matrix is a square orthogonal matrix that preserves vector lengths and angles under transformation.
- How it is used
- Transforms input features before machine-learning models to test model robustness and rotational behavior.
- How deep it goes
- Defines preservation and reversibility, then explains model consequences without deriving matrix construction.
- Examples
- Uses rotated tabular features to compare deep architectures with gradient-boosted decision trees.
- What you can do after
- Evaluate model behavior by applying reversible rotations and interpreting their effects on tree-based and deep models.
Related concepts
- orthogonalityequivalent to · Orthogonality is the relationship between vectors, directions, or states whose inner product is zero, corresponding to perpendicularity in Euclidean space.
- Rotary Position Embeddingused by · Rotary Position Embedding is a positional encoding method that represents token positions by applying position-dependent rotations to components of attention query and key vectors.
- coordinate systemaddresses · A coordinate system is a framework for specifying the positions of points or other geometric entities using numerical coordinates relative to defined references, such as an origin and axes.
- dimensionuses · A dimension is an independent coordinate, measurable axis, or descriptive attribute used to represent, locate, or analyze something.
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