Rectangular arrays that represent linear transformations and systems of equations compactly.
A matrix is an m×n array of numbers representing a linear map or a system of equations Ax=b. Special matrices include square, diagonal, identity, symmetric and triangular. Matrices store transformations, networks and data.
A rotation by θ is [[cosθ,-sinθ],[sinθ,cosθ]].
Matrices organise systems of equations and linear transformations, and they are the backbone of structural, circuit and control software.
Rectangular arrays that represent linear transformations and systems of equations compactly.
Matrices organise systems of equations and linear transformations, and they are the backbone of structural, circuit and control software.
It is a rectangular array of numbers that represents a linear map or a set of linear equations, and its entries can be forces, coefficients or measurements.
Libraries such as NumPy and MATLAB perform matrix operations very fast on hardware, so a whole system can be solved with one command.
Typical applications include assembling the stiffness matrix of a truss, writing the state equations of a robot arm and storing the pixels of a grayscale image as a matrix.
Study "Green, Stokes and divergence theorems" first (topic 47 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
Size is rows×columns. Identity leaves vectors unchanged. Symmetric matrices have real eigenvalues.
A rotation by θ is [[cosθ,-sinθ],[sinθ,cosθ]].
The next topic is "Matrix operations", which builds directly on this one.
It is classed as Intermediate in Engineering Mathematics (topic 48 of 104). It is an intermediate topic. Work through the beginner topics in Engineering Mathematics first.
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