A Square Matrix is Uniquely Expressible as the Sum of a Symmetric Matrix & a Skew-Symmetric Matrix скачать в хорошем качестве

A Square Matrix is Uniquely Expressible as the Sum of a Symmetric Matrix & a Skew-Symmetric Matrix

In this lecture on Linear Algebra, we prove an important theorem: “Every square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix.” In this video you will learn: • Definition of symmetric matrix • Definition of skew-symmetric matrix • Statement of the theorem • Step-by-step mathematical proof • How any square matrix A can be written as A = (A + Aᵀ)/2 + (A − Aᵀ)/2 This concept is very important for BSc Mathematics, Polytechnic, Engineering Mathematics and competitive exams. Watch the complete lecture to understand the concept clearly. Channel: MatheMagics #Matrix #LinearAlgebra #SymmetricMatrix #SkewSymmetricMatrix #Mathematics --- 3️⃣ Best Tags square matrix symmetric skew symmetric symmetric and skew symmetric matrix theorem decomposition of square matrix A = (A+A^T)/2 + (A-A^T)/2 linear algebra symmetric skew symmetric matrix theorem proof engineering mathematics matrices bsc mathematics matrices polytechnic mathematics matrix symmetric matrix proof skew symmetric matrix proof matrix decomposition theorem mathematics lecture matrices MatheMagics --- 4️⃣ Keywords square matrix theorem symmetric matrix skew symmetric matrix matrix decomposition linear algebra theorem matrices proof engineering mathematics matrices polytechnic maths matrices --- 5️⃣ Hashtags #Matrix #LinearAlgebra #SymmetricMatrix #SkewSymmetricMatrix #MatrixTheorem #EngineeringMathematics #BScMathematics #PolytechnicMaths #MatheMagics