Diagonal matrix
A diagonal matrix is a square matrix whose entries outside the main diagonal are zero.
Quantum Programming in Depth
A diagonal matrix is a square matrix whose entries outside the main diagonal are zero.
- How it is used
- Represents phase oracles and CS-decomposition components without mixing computational-basis states.
- How deep it goes
- Explains diagonal entries through single-qubit phase action, arbitrary-size CS constraints, and oracle behavior.
- Examples
- Uses C and S matrices, a single-qubit phase operation, and an oracle marking 001 and 110.
- What you can do after
- Evaluate/understand which basis-state amplitudes a diagonal quantum operation phases or sign-flips.
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Math and Architectures of Deep Learning
A square matrix whose only possibly nonzero entries are on the main diagonal.
- How it is used
- Supports diagonalization, coordinate rotation, quadratic-form analysis, and later PCA reasoning.
- How deep it goes
- Defines the structure and works through eigenvector-based diagonalization and geometric transformation, without developing numerical stability details.
- Examples
- Uses the ellipse 5x² + 6xy + 5y² = 20, its matrix [[5,3],[3,5]], and a 45° eigenvector rotation.
- What you can do after
- Apply PyTorch eigenvalue computation to rotate a symmetric quadratic form into diagonal, axis-aligned coordinates.
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Related concepts
- degree matrixincludes · A degree matrix is a diagonal graph matrix whose entries record the number or total weight of connections incident to each node.
- arraykind of · An array is an indexed, ordered collection of elements arranged in one or more dimensions, with elements accessed by position.
- Gaussian eliminationproduced by · Gaussian elimination is a procedure that applies elementary row operations to transform a linear system or matrix into an equivalent triangular or row-reduced form.
- covariance matrixconfigured by · A covariance matrix is a square matrix whose diagonal entries are variances and whose off-diagonal entries are pairwise covariances among variables.
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