The amount of calculus needed to understand linear algebra depends on the level of depth and complexity of the linear algebra concepts being studied. Some basic understanding of calculus, such as derivatives and integrals, is typically required for introductory linear algebra courses. As the level of linear algebra concepts increases, so does the level of calculus needed to understand them.
It is possible to learn some basic linear algebra concepts without knowing calculus, but a strong understanding of calculus is highly recommended for a thorough understanding of linear algebra. Many advanced linear algebra concepts, such as eigenvalues and eigenvectors, rely heavily on calculus concepts.
The most important calculus topics for understanding linear algebra include derivatives, integrals, and multivariable calculus concepts such as partial derivatives and gradients. A basic understanding of vector calculus is also helpful for more advanced linear algebra concepts.
Calculus and linear algebra are closely related fields of mathematics. Calculus is used to study continuous change, while linear algebra is used to study linear relationships and transformations. Many linear algebra concepts, such as matrix operations and systems of linear equations, can be solved using calculus methods.
Having a strong background in calculus can certainly be beneficial for excelling in linear algebra, as many advanced concepts in linear algebra require a solid understanding of calculus. However, with dedication and practice, it is possible to excel in linear algebra even without a strong background in calculus.