Linear Algebra skills & concepts to know for better grades 

Here are the important topics for Linear Algebra:

Vector Spaces

• Definition of a vector space
• Examples of vector spaces
• Linear operations on vectors
• Vector subspaces
• Linear independence and linear dependence
• Basis and dimension

Matrices

• Definition of a matrix
• Matrix operations
• Types of matrices
• Matrix inverses
• Linear systems of equations
• Matrix determinants

Linear Transformations

• Definition of a linear transformation
• The standard matrix of a linear transformation
• The kernel and image of a linear transformation
• The rank-nullity theorem

Eigenvalues and Eigenvectors

• Definition of eigenvalues and eigenvectors
• The characteristic polynomial
• The diagonalization of matrices

Inner Product Spaces

• Definition of an inner product space
• Orthogonality and projections
• Gram-Schmidt orthonormalization
• Least squares problems

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