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- 2025/5/24 18:58
- Experiencing the goodness of the matrix
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- A matrix can be said to be a linear system of equations with only coefficients, but if it has physical significance, the columns are seen first, then the rows as the change, such as a change in time or an increase in derivative.
Properties of Matrices When a column or a row is multiplied by k, the entire matrix is a scalar multiple of k.
It can be proved from the above that the matrix {c_ij}, which is the matrix AB=C multiplied by its components {a_ij} and {b_ij}, can be slightly modified to {a_kl-c} and {b_kl+c} in one place each, resulting in {c_kl-c^2}.
A matrix that is invertible (multiplied together to form a unitary matrix) is called a Hermite matrix, and we can prove that the first Hermite matrix × Hermite matrix is also a Hermite matrix.
Hermite matrices are defined as unitary matrices E=AA^(-1) and AB=C (C is also a Hermite matrix), but they are considered the same.
Diagonalization, which can speed up the computation of matrices, will be left for high school. In physical calculations, it can be calculated by multiplying by the Jordan matrix and then multiplying by the inverse of the Jordan matrix. The French reading is Jordan, but in English it is Jordan, but that does not mean that I am joking.
As one example of the significance of matrices in physical calculations of derivatives, let's look at a 4-dimensional electromagnetic potential.
We use the flux lines B, the voltage E and the following value of A
B=μ∇×A.E=-μ∇Φ-1/ε ∂B/∂A.
AΔA=X.XX*=ψΦψ*.X=hat(tr BB*)(taihimuler symbol)(Lagrangian Lagrangian)(ψΦψ*).
The detailed equations may not yet be clear to a junior or senior high school student.
- A matrix can be said to be a linear system of equations with only coefficients, but if it has physical significance, the columns are seen first, then the rows as the change, such as a change in time or an increase in derivative.
