Index notation describes vectors, matrices and tensors by their components relative to a chosen basis. For example, matrix multiplication reads . The free indices identify the resulting component, while is summed. An explicit summation sign avoids depending on an implicit Einstein summation convention.
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Index notation, also known as tensor notation or summation notation, is a mathematical notation used to represent vectors, matrices, and tensors in a compact and precise manner. It employs indices to denote the components of these mathematical objects, making it easier to manipulate and perform operations, especially in physics and engineering. ### Key Concepts of Index Notation: 1. **Components**: In index notation, a vector is represented by its components, with indices identifying each component.