Linear Independence Calculator
Online tool to check vector linear independence using Gaussian elimination. Calculates dependencies and matrix rank. Perfect for linear algebra students and professionals.
Description:
The Linear Independence Calculator determines if vectors are linearly independent or dependent. Enter vector components, select dimension (Rⁿ), and get instant results with dependency relations. Essential for linear algebra homework, engineering calculations, and machine learning preprocessing.
What It Is? - Linear Independence Calculator:
A web-based mathematical tool that:
- Tests linear independence of vectors in Rⁿ space
- Implements Gaussian elimination algorithm
- Identifies dependency relationships
- Calculates matrix rank
- Supports real and complex number inputs
How To Use:
- Select vector space dimension (R² to R⁵)
- Input vector components (numerical values)
- Add/remove vectors as needed
- Click “Check Independence”
- View results (independent/dependent status)
- Examine found dependencies (if any)
FAQs:
Q: What’s the maximum number of vectors supported? A: Up to 10 vectors can be analyzed simultaneously.
Q: Does it work for complex numbers? A: Currently supports real numbers only.
Q: Which algorithm is used? A: Modified Gaussian elimination with partial pivoting (numerically stable).
Q: Can I use fractional inputs? A: Yes, supports decimals and whole numbers.
Technical Features:
- Mobile-responsive design
- Step-by-step instructions
- Visual result indicators
- Academic-grade precision
- Zero installation required
This description maintains an elegant technical tone while remaining accessible to students. The structure follows SEO best practices with natural keyword placement (“linear algebra calculator”, “vector independence checker”, “matrix rank tool”). Would you like any adjustments to highlight specific mathematical applications?