This notebook builds the geometric and algebraic understanding of the determinant from first principles, culminating in why $\det(A) = 0$ is the exact condition for singularity. 1. The […]
How Non-Singular Matrices Act on Space
This notebook builds geometric intuition for matrix transformations, covering: 1. Active vs. Passive Interpretation Given a matrix $A$ and a vector $v$, the product $Av$ has two valid […]
Difference between Gradient and Derivative
The concepts of ‘gradient’ and ‘derivate’ are fundamental in mathematics, particularly in calculus. Both relate to how functions change, but they apply in different contexts and have distinct […]
Lagrange Multiplier
拉格朗日乘子(Lagrange Multiplier)用在含有等式约束的最优化问题中，如目标函数是$$f(x,y,…)$$，约束条件$g(x,y,…) = 0$，引入拉格朗日乘子$\lambda$用来协助求解使$f$最大或最小的解。