Contents • Vector spaces • Subspaces • Linear independence and span • Bases and dimension • Isomorphism and coordinate representation • Inner product and norm • Angles and orthogonality • Gram-Schmidt orthogonalisation process • Ohogonal projection and best approximation • Linear transrmations • Matrix representation of linear transrmations • Change of basis and similarity • Matrices as linear transrmations • Eigenvalues and eigenvectors • The characteristic polynomial • Matrix diagonalisation • Matrix exponential function A short summary of linear algebra and matrix theory Dr I M Jaimoukha
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Contents
• Vector spaces
• Subspaces
• Linear independence and span
• Bases and dimension
• Isomorphism and coordinate representation
• Inner product and norm
• Angles and orthogonality
• Gram-Schmidt orthogonalisation process
• Orthogonal projection and best approximation
• Linear transformations
• Matrix representation of linear transformations
• Change of basis and similarity
• Matrices as linear transformations
• Eigenvalues and eigenvectors
• The characteristic polynomial
• Matrix diagonalisation
• Matrix exponential function
A short summary of linear
algebra and matrix theory
Dr I M Jaimoukha
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