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Direct Sums and Matrix Representation - Revision. The (classical) Adjoint Matrix. Invariant Subspaces and Restriction of a Linear Operator. The Minimal Polynomial and Cayley - Hamilton Theorem. Primary Decomposition Theorem. Nilpotent Operator and The Index Of Nilpotency. Jordan Canonical Form and Matrix Similarity Over The Field of Complex Numbers. Inner Product Spaces. Orthogonal Complement and Gram - Schmidt Process. The Adjoint of an Operator And Self Adjoint - Operator. Orthogonal Projections. Unitary Operators and Isometries. Normal Operators. Spectral Decomposition And Orthogonal Diagonalization. Positive Definite Operators And Polar Decomposition. Linear Functionals and The Dual Space. Bilinear Forms and Quadratic Forms. Congruence of Matrices. The Determinant As a Volume Form. Additional Topics As Time Permits.

Faculty: Mathematics
|Undergraduate Studies

Pre-required courses

104066 - Algebra A or 104166 - Algebra Am

Course with no extra credit

104038 - Algebra 2m 104173 - Linear Algebra 2

Course with no extra credit (contained)

104171

Course with no extra credit (contains)

104168 - Algebra B

• Linear algebra - Hoffman, Kenneth
• Linear algebra : answers to problems - Hoffman, Kenneth
• Linear algebra and geometry - Kostrikin, Aleksei I.
• אלגברה א' - עמיצור, שמשון