Matrices
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See all →- What are symmetric and skew-symmetric matrices, and how is any square matrix written as their sum? In one line A square matrix is symmetric if A^T=A and skew-symmetric if A^T=-A ; every square matrix equals 1/2(A+A^T)+1/2(A-A^T) , a symmet... 1
- How do I find the inverse of a 3×3 matrix using the adjoint method? In one line If |A|≠0 , then A⁻¹=1/|A| adj A , where adj A is the transpose of the matrix of cofactors. Explained simply The inverse of a num... 1
- What are Hermitian and skew-Hermitian matrices and what properties do they have? In one line A complex square matrix is Hermitian if it equals its conjugate transpose ( A^θ=A ) and skew-Hermitian if A^θ=-A ; they are the... 1
- What are orthogonal and unitary matrices and how do I check whether a matrix is one? In one line A real matrix is orthogonal if AA^T=I (so A⁻¹=A^T ); a complex matrix is unitary if AA^θ=I (so A⁻¹=A^θ ). Explained simply Rotat... 1
- What is the rank of a matrix and how do elementary transformations help find it? In one line The rank of a matrix is the order of its largest non-zero minor, which equals the number of linearly independent rows; elementar... 1
- How do I find the rank of a matrix by reducing it to echelon form? In one line Use row operations to make the matrix upper-triangular in a staircase pattern (echelon form); the rank is the number of non-zero... 1