Linear Transformation Calculator
Transformation Matrix
Transformation Analysis
Determinant: 0
Transformed Vector: ( 0 , 0 )
Type: -
Understanding Linear Transformations
Linear transformations are functions that preserve vector addition and scalar multiplication, represented by matrices that transform vectors in a linear way.
Key Concepts
Matrix Properties
- Determinant analysis
- Eigenvalues
- Vector transformation
- Linear mapping
- Geometric effects
Transformation Types
- Rotation
- Scaling
- Reflection
- Shearing
- Projection
Applications
- Computer graphics
- Image processing
- Engineering analysis
- Physics simulations
- Data transformation
Matrix Analysis
- Determinant calculation
- Inverse matrices
- Eigendecomposition
- Singular values
- Basis transformation
Frequently Asked Questions
What is a linear transformation?
A linear transformation is a function between vector spaces that preserves vector addition and scalar multiplication, represented by a matrix multiplication.
What does the determinant tell us?
The determinant indicates how the transformation affects area. A positive determinant means orientation is preserved, while negative means it's reversed.
How do I interpret the results?
The transformed vector shows where your input vector lands after the transformation. The type indicates the geometric effect of the transformation.
Mathematical Disclaimer
This calculator provides basic linear transformation analysis. For advanced applications, consult with mathematical professionals.