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3: Cartesian Vectors and Tensors

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    • 3.1: Measuring space with Cartesian coordinates
      A convenient way to measure space is to assign to each point a label consisting of three numbers, one for each dimension.
    • 3.2: Vectors and Scalars
    • 3.3: Cartesian Tensors
      We have seen how to represent a vector in a rotated coordinate system. Can we do the same for a matrix? The basic idea is to identify a mathematical operation that the matrix represents, then require that it represent the same operation in the new coordinate system. We’ll do this in two ways: first, by seeing the matrix as a geometrical transformation of a vector, and second by seeing it as a recipe for a bilinear product of two vectors.

    This page titled 3: Cartesian Vectors and Tensors is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Bill Smyth via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.