Linear Algebra
Gram-Schmidt Process - Linear Algebra
Learn the gram-schmidt process with examples, step-by-step guide, and calculator tools. Orthogonalize vectors
The gram-schmidt process is a fundamental concept in linear algebra. Orthogonalize vectors. This page provides a comprehensive guide with worked examples and practical applications.
The Formula
\[\vec{u}_k = \vec{v}_k - \sum_{j=1}^{k-1} \text{proj}_{\vec{u}_j}(\vec{v}_k)\]
Variables
u⃗ₖ
Orthogonal vector
v⃗ₖ
Original vector
Step-by-Step Guide
- 1
Step 1: Gather your data values
- 2
Step 2: Apply the formula
- 3
Step 3: Perform the calculations
- 4
Step 4: Interpret the result
Examples
Example 1
Example 1: [] → Creates orthogonal basis from any basis
Example 2
Example 2: Orthogonal basis
Frequently Asked Questions
What is the gram-schmidt process?
Orthogonalize vectors
How do I calculate gram-schmidt process?
Use the formula: \vec{u}_k = \vec{v}_k - \sum_{j=1}^{k-1} \text{proj}_{\vec{u}_j}(\vec{v}_k). Follow the steps provided above.
What tools can help with gram-schmidt process?
We provide online calculators: calculator